An interference pattern is formed on a screen when light of
wavelength 500 nm is incident on two parallel slits 60
μmapart.
Find the angle of the third order bright fringe.

When an electron is accelerated from rest through a potential difference of 9.9 kV, its resulting speed is approximately 5.9 x 10⁷ m/s.

The resulting speed of an electron accelerated through a potential difference can be calculated using the formula [tex]v = \sqrt{(2qV/m)}[/tex], where v is the speed, q is the charge of the electron, V is the potential difference, and m is the mass of the electron.
In this case, the charge of the electron (q) is [tex]1.60 \times 10^{-19} C[/tex], and the potential difference (V) is 9.9 kV, which can be converted to volts by multiplying by 1000. The mass of the electron (m) is [tex]9.11 \times 10^{-31} kg[/tex].

Plugging these values into the formula, we get [tex]v = \sqrt{(\frac {2 \times 1.60 \times 10^{-19} C \times 9900 V}{9.11 \times 10^{-31} kg}}[/tex]. Evaluating this expression gives us v ≈ 5.9 x  10⁷ m/s.

Therefore, the resulting speed of the electron accelerated through a potential difference of 9.9 kV is approximately 5.9 x 10⁷ m/s.

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The complete question is:

If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? [tex](e = 1.60 \times 10{-19} C, k= 8.99 \times 10^9 N \cdot m^2/C^2, m_{el} = 9.11 \times 10^{-31} kg)[/tex]

A. 5.9 x 10⁷ m/s B. 2.9 x 10⁷ m/s C. 4.9 x 10⁷ m/s D. 3.9 x 10⁷ m/s

Given a change in magnetic field from 2.30 T to 5.50 T over a time period of 4.50 s, and a wire loop with an area of 0.350 m²,The average induced emf in the wire loop is 5.33 V.

According to Faraday's law, the induced emf in a wire loop is equal to the rate of change of magnetic flux through the loop. The magnetic flux (Φ) is given by the product of the magnetic field (B) and the area of the loop (A). In this case, the magnetic field changes from 2.30 T to 5.50 T, so the change in magnetic field (ΔB) is 5.50 T - 2.30 T = 3.20 T.

The average induced emf (ε) can be calculated using the formula:

ε = ΔΦ / Δt

where ΔΦ is the change in magnetic flux and Δt is the change in time. The change in time is given as 4.50 s.

To find the change in magnetic flux, we multiply the change in magnetic field (ΔB) by the area of the loop (A):

ΔΦ = ΔB * A

Plugging in the values, we have:

ΔΦ = 3.20 T * 0.350 m² = 1.12 Wb (weber)

Finally, substituting the values into the formula for average induced emf, we get:

ε = 1.12 Wb / 4.50 s = 5.33 V

Therefore, the average induced emf in the wire loop is 5.33 V.

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The radius of Satellite Rock B's orbit (RB) is approximately 522.47 km.

To determine the radius of Satellite Rock B's orbit (RB), we can use Kepler's Third Law of Planetary Motion, which relates the orbital period and orbital radius of celestial bodies. Kepler's Third Law states that the square of the period (T) of an object in an orbit is proportional to the cube of its orbital radius (R).

Mathematically, it can be expressed as: T² ∝ R³

Given that Satellite Rock A has an orbital radius of R₁ = 280.0 km and a period of TA, we can write the following equation: TA² = R₁³

Now, let's consider Satellite Rock B. We are given that it takes Rock B a time TB = 3.78TA to orbit the asteroid once. Using the same equation, we can write: TB² = RB³

Since we want to find RB, we can rearrange the equation:

RB = (TB²)^(1/3)

Substituting the value of TB = 3.78TA, we get:

RB = (3.78TA²)^(1/3)

Since we know that TA² = R₁³, we can substitute this into the equation:RB = (3.78 * R₁³)^(1/3)

Now we can calculate the value of RB using the given radius of Satellite Rock A: RB = (3.78 * (280.0 km)³)^(1/3)

RB ≈ 522.47 km

Therefore, the radius of Satellite Rock B's orbit (RB) is approximately 522.47 km.

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The rate of reinforced refrigeration would be -0.088 mass flow rate of R-134a kW , Where the negative sign indicates refrigeration.The mass flow of R 134-a required would be  11 g/s. Exergy destruction in evaporator would be 0.71 kW, in compressor would be 0.018 kW.

Given conditions:

R-134-a will be used to fulfill the cooling of the bananas.The evaporator will work at 100 kPa with a superheat of 6.4°C and an efficiency of 80%.The compressor will have a compression ratio of 9 with isentropic efficiency of 85%.

a) Rate of refrigeration

Refrigeration is the process of cooling a space or substance below the environmental temperature. The unit of refrigeration is ton of refrigeration (TR).1 TR = 211 kJ/minRate of refrigeration can be calculated as follows:

Rate of refrigeration = (mass flow rate of R-134a × enthalpy difference at evaporator) / 1000

Rate of refrigeration = (mass flow rate of R-134a × h2-h1) / 1000

Where

h1 = Enthalpy at the evaporator inlet

h2 = Enthalpy at the evaporator outlet

Enthalpy values can be obtained from the refrigerant table of R-134a.

From the refrigerant table of R-134a,

At evaporator inlet (saturation state):

P = 100 kPa, superheat = 6.4°C h1 = 286.7 kJ/kg

At evaporator outlet (saturated state):

P = 100 kPa

h2 = 198.6 kJ/kg

Rate of refrigeration = (mass flow rate of R-134a × (198.6 - 286.7)) / 1000

Rate of refrigeration = -0.088 mass flow rate of R-134a kW

Where the negative sign indicates refrigeration.

b) Mass flow rate of R-134a

The mass flow rate of R-134a can be obtained as follows:

Mass flow rate of R-134a = Rate of refrigeration / (enthalpy difference at compressor/ηC)

Mass flow rate of R-134a = Rate of refrigeration / (h3 - h4s / ηC)Where

ηC is the isentropic efficiency of the compressor

From the refrigerant table of R-134a,

At compressor inlet (saturated state):

P = 100 kPa

h3 = 198.6 kJ/kg

At compressor outlet (saturation state):

P = 900 kPa

h4s = 323.4 kJ/kgηC = 85%

Mass flow rate of R-134a = -0.088 / (323.4 - 198.6 × 0.85)

Mass flow rate of R-134a = 0.011 kg/s

Mass flow rate of R-134a = 11 g/s

Therefore, the mass flow rate of R-134a is 11 g/s.

c) Exergy destruction in each basic component

The formula for the exergy destruction in each basic component is given by the following equation:

Exergy destruction in evaporator = mR × (h2 - h1 - T0 × (s2 - s1))

Exergy destruction in compressor = mR × (h3s - h4 - T0 × (s3s - s4))

Where mR is the mass flow rate of R-134aT

0 is the temperature at the surroundings/sink

From the refrigerant table of R-134a,

At evaporator inlet (saturation state):

P = 100 kPa, superheat = 6.4°C

h1 = 286.7 kJ/kg

s1 = 1.0484 kJ/kg K

At evaporator outlet (saturated state):

P = 100 kPa

h2 = 198.6 kJ/kg

s2 = 0.8369 kJ/kg K

At compressor inlet (saturated state):

P = 100 kPa

h3 = 198.6 kJ/kg

s3 = 0.6689 kJ/kg K

At compressor outlet (saturation state):

P = 900 kPa

h4s = 323.4 kJ/kg

s4 = 1.5046 kJ/kg K

Exergy destruction in evaporator = 0.011 × (198.6 - 286.7 - 27 + 6.4 × (0.8369 - 1.0484))

Exergy destruction in evaporator = 0.71 kW

Exergy destruction in compressor = 0.011 × (198.6 - 323.4 + 27 - (0.85 × (198.6 - 323.4 + 27) + (1 - 0.85) × (0.6689 - 1.5046)))

Exergy destruction in compressor = 0.018 kW

Therefore, the exergy destruction in the evaporator is 0.71 kW and the exergy destruction in the compressor is 0.018 kW.

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The magnitude of the electrostatic force acting between two tiny, spherical water drops with identical charges of -4.89 x 10⁻¹⁶ C and a center-to-center separation of 1.33 cm is 5.35 x 10⁻¹³ N.

The magnitude of the electrostatic force acting between two tiny, spherical water drops with identical charges of -4.89 x 10^-16 C and a center-to-center separation of 1.33 cm is 5.35 x 10⁻¹³ N.

Electrostatic force is the force that develops between two or more electrically charged bodies. These forces arise as a result of the interaction of charged bodies. Coulomb's law expresses the electrostatic force that develops between two electrically charged particles.

Coulomb's law is a fundamental law of electrostatics that describes the interaction between charged particles. According to this law, the magnitude of the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The formula for electrostatic force is: F = (k * q1 * q2) / r2where F is the electrostatic force, k is Coulomb's constant, q1 and q2 are the charges of the two particles, and r is the distance between them.

Coulomb's constant is a proportionality constant that is used to describe the electrostatic force between two charged particles. The value of Coulomb's constant is approximately 8.99 x 10⁹ N·m2/C2.

The distance between the two tiny, spherical water drops, r = 1.33 cm = 0.0133 mThe charge on each drop, q1 = q2 = -4.89 x 10⁻¹⁶ C

The Coulomb constant, k = 8.99 x 10⁹ N·m2/C2

Substituting the given values in the Coulomb's law formula,

F = (k * q1 * q2) / r2F = (8.99 × 10⁹ × (-4.89 × 10⁻¹⁶)²) / (0.0133)²F = 5.35 × 10⁻¹³ N

Therefore, the magnitude of the electrostatic force acting between two tiny, spherical water drops with identical charges of -4.89 x 10⁻¹⁶ C and a center-to-center separation of 1.33 cm is 5.35 x 10⁻¹³ N.

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The type of radiation that you should be concerned about when shielded by a quarter inch thick aluminum sheet is gamma radiation.

Alpha radiation consists of alpha particles, which are large and heavy particles consisting of two protons and two neutrons. They have a relatively low penetrating power and can be stopped by a sheet of paper or a few centimeters of air.

Beta radiation, on the other hand, consists of high-speed electrons or positrons and can be stopped by a few millimeters of aluminum.

However, gamma radiation is a type of electromagnetic radiation that consists of high-energy photons. It has a much higher penetrating power compared to alpha and beta radiation. To shield against gamma radiation, materials with higher atomic numbers, such as lead or thick layers of concrete, are required.

While a quarter inch thick aluminum sheet can provide some shielding against gamma radiation, it may not be sufficient to provide complete protection. Therefore, gamma radiation is the type of radiation you should be concerned about in this scenario.

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The probability of finding a particle in any of the three energy states is the same everywhere inside the box.

The probability of finding a particle in any of the three energy states is the same everywhere inside the box. Consider the normalised eigenstates for a particle in a 1-dimensional box as shown: Eigenstates. The normalised eigenstates for a particle in a 1-dimensional box are as follows:Here, A is the normalization constant.\

To find the probability of finding a particle in any of the three energy states, we need to find the probability density function (PDF), ψ²(x).Probability density function (PDF), ψ²(x) is given as follows:Here, ψ(x) is the wave function, which is the normalised eigenstate for a particle in a 1-dimensional box.

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The man does approximately 35.28 Joules of work while holding the watermelon steady above his head.

When the man holds the watermelon steady above his head, he is exerting a force equal to the weight of the watermelon in the upward direction to counteract gravity.

The work done by the man can be calculated using the formula:

Work = Force × Distance × cosθ

Where:

Force is the upward force exerted by the man (equal to the weight of the watermelon),

Distance is the vertical distance the watermelon is lifted (1.8 m),

θ is the angle between the force and the displacement vectors (which is 0 degrees in this case, since the force and displacement are in the same direction).

Mass of the watermelon (m) = 2 kg

Acceleration due to gravity (g) = 9.8 m/s^2

Distance (d) = 1.8 m

Weight of the watermelon (Force) = mass × gravity

Force = 2 kg × 9.8 m/s^2

Force = 19.6 N

Now we can calculate the work done by the man:

Work = Force × Distance × cosθ

Work = 19.6 N × 1.8 m × cos(0°)

Work = 19.6 N × 1.8 m × 1

Work = 35.28 Joules

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The weak force and the electromagnetic force are two fundamental forces in nature that have distinct characteristics. One notable contrast between them is their range of influence.

The weak force acts within the nucleus of an atom, specifically within protons and neutrons, and has a very short-range, limited to distances on the order of nuclear dimensions.

In contrast, the electromagnetic force has an infinite range, meaning it can act over long distances, reaching out to infinity.

Furthermore, the nature of the forces' interactions differs. The weak force is both attractive and repulsive, meaning it can either attract or repel particles depending on the circumstances.

On the other hand, the electromagnetic force is solely attractive, leading to the attraction of charged particles and the binding of electrons to atomic nuclei.

In summary, the weak force acts within protons and neutrons, with a limited range, and exhibits both attractive and repulsive behavior, while the electromagnetic force has an infinite range, acts between charged particles, and is exclusively attractive.

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To calculate the total work done by the gas, we need to use the formula

W = -PΔV

where W is work,

P is pressure, and ΔV is the change in volume.

Since pressure is constant, we can use the initial pressure value of 2.5 atm to calculate the work done.

W = -PΔV = -(2.5 atm) (0.65 L - 0.5 L) = -0.375 L-atm

We can express the answer to two significant figures as

W = -0.38 L-atm

To calculate the total heat flow into the gas, we need to use the first law of thermodynamics which states that

ΔU = Q + W

where ΔU is the change in internal energy, Q is the heat flow, and W is the work done.

Since the gas returns to its original temperature, we know that

ΔU = 0

which means that

Q = -W

Using the value of work done from Part A, we can calculate the heat flow as

Q = -W = 0.38 L-atm

We can express the answer to two significant figures as

Q = 0.38 L-atm.

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In the given double-slit experiment with electrons, the separation between the two slits is 0.020 μm.

The first-order minimum (dark fringe) is observed at an angle of 8.63 degrees relative to the incident electron beam. The task is to determine the wavelength of the moving electrons (Part A) and the momentum of each moving electron (Part B).

Part A: To find the wavelength of the moving electrons, we can use the formula for the wavelength of a particle diffracted by a double slit, given by λ = (d * sinθ) / n, where λ is the wavelength, d is the separation between the slits, θ is the angle of the first-order minimum, and n is the order of the minimum (which is 1 in this case). By substituting the given values, we can calculate the wavelength of the moving electrons.

Part B: The momentum of each moving electron can be determined using the de Broglie wavelength equation, which states that the momentum of a particle is equal to h / λ, where h is Planck's constant. By substituting the calculated wavelength from Part A into the equation, we can find the momentum of each moving electron in scientific notation format.

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The intensity of sound is [tex]$I_1 = 0.1 \, \text{W/m}^2$[/tex]. the sound intensity at a distance of 500 m from the jet is [tex]$I_2 = 0.00064 \, \text{W/m}^2$[/tex]. the sound intensity level at a distance of 500 m from the jet is [tex]$L_2 = 28.06 \, \text{dB}$[/tex].

Given:

Sound intensity level at a distance of 40 m, L1 = 110 dB

To find:

a) Intensity of sound in units of W/m².

b) Power of the jet engine in units of Watts.

c) Sound intensity at a distance of 500 m from the jet.

d) Sound intensity level at a distance of 500 m from the jet.

Conversion formulas:

Sound intensity level (in dB): L = 10 log10(I/I0)

Sound intensity (in W/m²): I = I0 × [tex]10^{(L/10)[/tex]

where I0 is the reference intensity (in W/m²), which is [tex]10^{(-12)[/tex] W/m².

a) To calculate the intensity of sound:

Using the formula for sound intensity:

I = I0 × [tex]10^{(L/10)[/tex]

Given L1 = 110 dB and I0 = [tex]10^{(-12)[/tex] W/m²,

I1 = ([tex]10^{(-12)[/tex] W/m²) × [tex]10^{(110/10)[/tex]

Calculating the value of I1:

I1 = [tex]10^{(-12 + 11)[/tex]

I1 = [tex]10^{(-1)[/tex] W/m²

I1 = 0.1 W/m²

Therefore, the intensity of sound is [tex]$I_1 = 0.1 \, \text{W/m}^2$[/tex].

b) To calculate the power of the jet engine:

Power (P) is the rate at which energy is transferred or work is done. Power is related to intensity (I) by the formula:

P = I × A

where A is the area over which the sound is distributed.

Since we are not given the area, we cannot directly calculate the power without additional information.

c) To calculate the sound intensity at a distance of 500 m from the jet:

Using the inverse square law, the sound intensity decreases with the square of the distance:

I2 = I1 × [tex](r1/r2)^2[/tex]

Given r1 = 40 m, r2 = 500 m, and I1 = 0.1 W/m²,

I2 = 0.1 W/m² × [tex](40/500)^2[/tex]

Calculating the value of I2:

I2 = 0.1 W/m² × [tex](0.08)^2[/tex]

I2 = 0.00064 W/m²

Therefore, the sound intensity at a distance of 500 m from the jet is [tex]$I_2 = 0.00064 \, \text{W/m}^2$[/tex].

d) To calculate the sound intensity level at a distance of 500 m from the jet:

Using the formula for sound intensity level:

L2 = 10 log10(I2/I0)

Given I2 = 0.00064 W/m² and I0 = [tex]10^{(-12)[/tex] W/m²,

L2 = 10 log10(0.00064/[tex]10^{(-12)}[/tex])

Calculating the value of L2:

L2 = 10 log10(0.00064 × [tex]10^{12[/tex])

L2 = 10 log10(0.64 × [tex]10^3[/tex])

L2 = 10 log10(640)

L2 = 10 × 2.806

L2 = 28.06 dB

Therefore, the sound intensity level at a distance of 500 m from the jet is [tex]$L_2 = 28.06 \, \text{dB}$[/tex].

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The intensity of sound is . the sound intensity at a distance of 500 m from the jet is . the sound intensity level at a distance of 500 m from the jet is .

Given:

Sound intensity level (SIL) of jet engine at 40 m: 110 dB

Distance from the jet engine: 40 m

To find the intensity of sound in units of W/m^2, we can use the formula:

I = I₀ * 10^(SIL/10)

where I₀ is the reference intensity, which is generally taken as 1 x 10^(-12) W/m^2 for sound.

Calculating the intensity at 40 m:

I = (1 x 10^(-12) W/m^2) * 10^(110/10)

I ≈ 1.00 W/m^2 (to two decimal places)

The power of the jet engine mentioned in Part A can be calculated by multiplying the intensity by the surface area. Since we don't have the surface area mentioned, we cannot determine the exact power value in watts.

To find the sound intensity at a distance of 500 m from the jet engine, we can use the inverse square law, which states that the intensity decreases with the square of the distance. The formula is:

I₂ = I₁ * (d₁/d₂)^2

where I₁ is the initial intensity at distance d₁, and I₂ is the intensity at distance d₂.

Calculating the intensity at 500 m:

I₂ = 1.00 W/m^2 * (40 m / 500 m)^2

I₂ ≈ 0.064 W/m^2 (in scientific notation with two decimal places)

The sound intensity level (SIL) at the new distance can be calculated using the formula:

SIL₂ = 10 * log10(I₂/I₀)

Calculating the SIL at 500 m:

SIL₂ = 10 * log10(0.064 W/m^2 / (1 x 10^(-12) W/m^2))

SIL₂ ≈ 106.69 dB (in scientific notation with four significant figures)

Therefore:

The intensity of sound in units of W/m^2 at 40 m is approximately 1.00 W/m^2.

The power of the jet engine cannot be determined without the surface area.

The sound intensity at a distance of 500 m from the jet engine is approximately 0.064 W/m^2.

The sound intensity level (SIL) of the jet engine at the new distance of 500 m is approximately 106.69 dB.

Therefore, the sound intensity level at a distance of 500 m from the jet is .

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the speed parameters β for the given Lorentz factors are: (a) 0.346, (b) 0.982, (c) 0.9999, and (d) 1.0.

To calculate the speed parameter (β) from the given Lorentz factor (γ), we use the formula β = √(γ^2 - 1).

(a) For a Lorentz factor of 1.0279127:

Plugging the value into the formula: β = √(1.0279127^2 - 1)

Calculating: β ≈ √(1.05601137 - 1)

β ≈ √0.05601137

β ≈ 0.346

(b) For a Lorentz factor of 7.7044323:

Plugging the value into the formula: β = √(7.7044323^2 - 1)

Calculating: β ≈ √(59.46321612 - 1)

β ≈ √(58.46321612)

β ≈ 0.982

(c) For a Lorentz factor of 138.79719:

Plugging the value into the formula: β = √(138.79719^2 - 1)

Calculating: β ≈ √(19266.21944236 - 1)

β ≈ √(19266.21944236)

β ≈ 0.9999

(d) For a Lorentz factor of 978.83229:

Plugging the value into the formula: β = √(978.83229^2 - 1)

Calculating: β ≈ √(957138.51335084 - 1)

β ≈ √(957137.51335084)

β ≈ 1.0

Therefore, the speed parameters β for the given Lorentz factors are: (a) 0.346, (b) 0.982, (c) 0.9999, and (d) 1.0.

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When the value of the distance from the image to the lens is negative, it implies that the image formed by the lens is option (A), virtual. In optics, a virtual image is an image that cannot be projected onto a screen but is perceived by the observer as if it exists.

It is formed by the apparent intersection of the extended light rays, rather than the actual convergence of the rays. The negative distance indicates that the image is formed on the same side of the lens as the object. In other words, the light rays do not physically converge but appear to diverge after passing through the lens. This occurs when the object is located closer to the lens than the focal point. Furthermore, a virtual image formed by a lens is always upright, meaning that it has the same orientation as the object. However, it is important to note that the virtual image is reduced in size compared to the object. The reduction in size occurs because the virtual image is formed by the apparent intersection of the diverging rays, resulting in a magnification less than 1. Therefore, when the value of the distance from the image to the lens is negative, it indicates the formation of a virtual image that is upright and reduced in size with respect to the object.

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The average mass of 235U needed to provide power for the average American family for one year is 1.15 x 10^-6 kg.

The amount of joules used in one year by the average American family is around 3.75 x 10^7 J. The energy that would be released if 1.02 kg of 235U undergoes fission is 3.24 x 10^13 J. Therefore, to produce the amount of energy needed for the average American family, 3.75 x 10^7 J ÷ 3.24 x 10^13 J/kg = 1.15 x 10^-6 kg of 235U is needed.

So, the average mass of 235U needed to provide power for the average American family for one year is 1.15 x 10^-6 kg. The calculation implicitly assumes perfect conversion to usable power, which is never the case in real systems. Enough uranium deposits are known so as to provide the world's current energy requirements for a few hundred years. Breeder reactor technology can greatly extend those reserves.

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The magnitude of the electrostatic force on a third charge placed at a specific location can be calculated using Coulomb's law.

In this case, a charge of +54 µC is located at x = 0, a charge of -38 µC is located at x = 50 cm, and a third charge of 4.0 µC is located at x = 15 cm on the x-axis. By applying Coulomb's law, the magnitude of the electrostatic force can be determined.

Coulomb's law states that the magnitude of the electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as F = k * |q1 * q2| / r^2, where F is the electrostatic force, q1, and q2 are the charges, r is the distance between the charges, and k is the electrostatic constant.

In this case, we have a charge of +54 µC at x = 0 and a charge of -38 µC at x = 50 cm. The third charge of 4.0 µC is located at x = 15 cm. To calculate the magnitude of the electrostatic force on the third charge, we need to determine the distance between the third charge and each of the other charges.

The distance between the third charge and the +54 µC charge is 15 cm (since they are both on the x-axis at the respective positions). Similarly, the distance between the third charge and the -38 µC charge is 35 cm (50 cm - 15 cm). Now, we can apply Coulomb's law to calculate the electrostatic force between the third charge and each of the other charges.

Using the equation F = k * |q1 * q2| / r^2, where k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2), q1 is the charge of the third charge (4.0 µC), q2 is the charge of the other charge, and r is the distance between the charges, we can calculate the magnitude of the electrostatic force on the third charge.

Substituting the values, we have F1 = (9 x 10^9 Nm^2/C^2) * |(4.0 µC) * (54 µC)| / (0.15 m)^2, where F1 represents the force between the third charge and the +54 µC charge. Similarly, we have F2 = (9 x 10^9 Nm^2/C^2) * |(4.0 µC) * (-38 µC)| / (0.35 m)^2, where F2 represents the force between the third charge and the -38 µC charge.

Finally, we can calculate the magnitude of the electrostatic force on the third charge by summing up the forces from each charge: F_total = F1 + F2.

Performing the calculations will provide the numerical value of the magnitude of the electrostatic force on the third charge in whole numbers.

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The wavelength of the light is determined to be 12.73 nm (nanometers). The angle at which the first order will appear is approximately 21.08°.

Diffraction grating with 4500 lines/cm

Third order of a wavelength appears at 10ºWe have to determine the wavelength and then determine at what angle the first order will appear.

1: Calculating the Wavelength

Formula to calculate the wavelength is given by:dsinθ = nλHere, d = 1/N, where N is the number of lines per unit length, i.e., d = 1/4500 = 0.000222 m.

θ = 10º (given)

n = 3 (third order)

λ = ?d × sin θ = nλ0.000222 × sin 10° = 3λ

λ = 0.00000001273 m = 12.73 nm

2: Calculating the Angle for the First OrderWe know that the angle of diffraction for the first order is given by:dsinθ = λ

Here, d = 1/N, where N is the number of lines per unit length, i.e., d = 1/4500 = 0.000222 m.

λ = 12.73 nm = 12.73 × 10^−9 m

θ = ?

d × sin θ = λsin

θ = λ/dθ = sin−1(λ/d)

θ = sin−1(12.73 × 10^−9 / 0.000222)

θ = 21.08° (approx)

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The paraffin wax will expand by approximately 4.5 grams in 10 seconds, and it will take approximately 1 hour and 40 minutes to fully expand.

Paraffin wax expands when heated due to the phase change from solid to liquid. Given that the activation temperature of the paraffin wax is 17°C and its melting point is 50°C, we can calculate the expansion rate.

Calculate the amount of expansion in 10 seconds.

The expansion rate of paraffin wax is 15%. So, if we have 30 grams of paraffin wax, the expansion in 10 seconds can be calculated as follows:

Expansion in 10 seconds = 15% of 30 grams = (15/100) * 30 grams = 4.5 grams.

Calculate the time required for full expansion.

To determine the time required for the paraffin wax to fully expand, we need to consider the rate at which it expands. Since we know the expansion rate and the amount of wax, we can calculate the time as follows:

Total expansion = 15% of 30 grams = (15/100) * 30 grams = 4.5 grams.

To fully expand from its solid state to liquid, the paraffin wax needs to go through the entire phase change process, which takes time. Unfortunately, the provided information does not specify the specific rate of expansion or the time required for the paraffin wax to reach its melting point.

In general, the time required for full expansion depends on various factors such as the amount of wax, the rate of heating, the surroundings, and the thermal conductivity. Therefore, without additional information, it is not possible to determine the exact time required for the paraffin wax to fully expand.

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The index of refraction of the unknown transparent liquid is 1.21. When a ray of light goes from one medium into another, it bends or refracts at the boundary of the two media. The angle at which the incident ray approaches the boundary line is known as the angle of incidence, and the angle at which it refracts into the second medium is known as the angle of refraction.

The index of refraction for a material is a measure of how much the speed of light changes when it passes from a vacuum to the material. It may also be stated as the ratio of the speed of light in a vacuum to the speed of light in the material. It may also be used to determine the degree to which light is bent or refracted when it passes from one material to another with a different index of refraction. The following is the answer to the question:A ray of light travelling through the unknown transparent liquid has an incident angle of 20.0° and is then refracted to 22.1° upon reaching the water below.

The index of refraction for the unknown transparent liquid can be found using the following equation:

n1sinθ1 = n2sinθ2

where,θ1 is the angle of incidence,θ2 is the angle of refraction,n1 is the index of refraction of the first medium,n2 is the index of refraction of the second medium.

By substituting the values of θ1, θ2, and n1 into the above equation, we get:

n2 = n1 sin θ1 / sin θ2n1 = 1.33 (given)

n2 = n1 sin θ1 / sin θ2

= 1.33 sin 20.0° / sin 22.1°

= 1.21 to three significant figures.

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The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

A.  In this case, if the immersed object displaces 8 N of fluid, then the buoyant force on the block is also 8 N. This is known as Archimedes' principle, which states that the buoyant force experienced by an object in a fluid is equal to the weight of the fluid displaced by the object.

B. To exert the smallest pressure against a table, you should place the screw in a way that maximizes the surface area of contact between the screw and the table. By spreading the force over a larger area, the pressure exerted by the screw on the table is reduced. This is based on the equation for pressure, which is equal to force divided by area (P = F/A). Therefore, by increasing the contact area (denominator), the pressure decreases.

C. When an object with a volume of 100 cm³ is submerged in a swimming pool, the volume of water displaced will also be 100 cm³. This is because according to Archimedes' principle, the volume of fluid displaced by an object is equal to the volume of the object itself. So, when the object is submerged, it displaces an amount of water equal to its own volume.

D. When you apply a flame to 1 L of water for a certain time and its temperature rises by 2°C, if you apply the same flame for the same time to 2 L of water, its temperature increase will be the same, 2°C. This is because the change in temperature depends on the amount of heat energy transferred to the water, which is determined by the flame's heat output and the time of exposure. The volume of water being heated does not affect the change in temperature, as long as the same amount of heat energy is transferred to both volumes of water.

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Energy and power are related concepts in physics, but they represent different aspects of a system. Energy refers to the capacity to do work or the ability to produce a change.

It is a scalar quantity and is measured in units such as joules (J) or kilowatt-hours (kWh). Energy can exist in various forms, such as kinetic energy (associated with motion), potential energy (associated with position or state), thermal energy (associated with heat), and so on.

Power, on the other hand, is the rate at which energy is transferred, converted, or used. It is the amount of energy consumed or produced per unit time. Power is a scalar quantity measured in units such as watts (W) or kilowatts (kW).

It represents how quickly work is done or energy is used. Mathematically, power is defined as the ratio of energy to time, so it can be expressed as P = E/t.

To illustrate the difference between energy and power, let's consider the example of a light bulb. The energy consumed by the light bulb is measured in kilowatt-hours (kWh) and represents the total amount of electrical energy used over a period of time.

The power rating of the light bulb is measured in watts (W) and indicates the rate at which electrical energy is converted into light and heat. So, if a light bulb has a power rating of 60 watts and is switched on for 5 hours, it will consume 300 watt-hours (0.3 kWh) of energy.

Similarly, in the case of an electric motor, the energy consumed would be measured in kilowatt-hours (kWh), representing the total amount of electrical energy used to perform work.

The power of the motor, measured in kilowatts (kW), would indicate how quickly the motor can convert electrical energy into mechanical work. The higher the power rating, the more work the motor can do in a given amount of time.

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(a) The de Broglie wavelength of a proton moving at a speed of 2.07 x 10⁴ m/s is approximately 3.34 x 10⁻¹¹ m.

(b) The relativistic relationship between momentum (p) and speed (v) is p = γ × m × v, where γ is the gamma factor. The gamma factor for a proton moving at a speed close to the speed of light can be calculated using γ = 1 / √(1 - (v² / c²)), where c is the speed of light (approximately 3.00 x 10⁸ m/s). The de Broglie wavelength can be calculated using the de Broglie wavelength formula λ = h / p, where h is Planck's constant.

(c) The de Broglie wavelength for a relativistic electron with a kinetic energy of 3.35 MeV is approximately 4.86 x 10⁻¹² m.

(a) To calculate the de Broglie wavelength of a proton, we can use the formula:

λ = h / p

where λ is the de Broglie wavelength, h is the Planck's constant, and p is the momentum of the proton.

v = 2.07 x 10⁴ m/s

To find the momentum of the proton, we can use the formula:

p = m × v

where m is the mass of the proton.

The mass of a proton is approximately 1.67 x 10⁻²⁷ kg.

Substituting the values into the formula:

p = (1.67 x 10⁻²⁷ kg) × (2.07 x 10⁴ m/s)

Now we can calculate the de Broglie wavelength:

λ = h / p

Given that h = 6.63 x 10⁻³⁴ J·s, we can substitute the values and calculate the wavelength.

(b) For the case of a proton moving at a speed close to the speed of light, we need to consider the relativistic relationship between momentum (p) and speed (v):

p = γ × m × v

where γ is the gamma factor, m is the mass of the proton, and v is the speed of the proton.

The gamma factor is given by:

γ = 1 / √(1 - (v² / c²))

where c is the speed of light, approximately 3.00 x 10⁸ m/s.

Given the speed of the proton as v = 2.16 x 10⁸ m/s, we can calculate the gamma factor (γ) using the above formula.

Once we have the gamma factor, we can use it in the de Broglie wavelength formula to find the wavelength.

(c) To find the de Broglie wavelength of a relativistic electron with a kinetic energy, we can use the equation:

λ = h / √(2 × m × KE)

where λ is the de Broglie wavelength, h is the Planck's constant, m is the mass of the electron, and KE is the kinetic energy of the electron.

The mass of an electron is approximately 9.11 x 10⁻³¹ kg.

Given the kinetic energy as 3.35 MeV, we need to convert it to joules by multiplying by the conversion factor 1 MeV = 1.6 x 10⁻¹³ J.

Once we have the values, we can substitute them into the formula to calculate the de Broglie wavelength.

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In physics, the magnitude of a force refers to the numerical value or size of the force without considering its direction. The magnitude of the force on the 110 m section of the power line is approximately 34,495.88 N.

It represents the strength or intensity of the force acting on an object. Magnitude is a scalar quantity, meaning it only has magnitude and no specific direction.

When calculating the magnitude of a force, you ignore any directional information and focus solely on the numerical value. For example, if a force of 20 Newtons is applied to an object, the magnitude of the force is simply 20 N, regardless of whether the force is acting horizontally, vertically, or at any angle.

To calculate the magnitude of the force on a section of the power line, we can use the formula:

[tex]F = I * L * B * sin(\theta)[/tex]

where:

F is the force (in N),

I is the current in the power line (in A),

L is the length of the section (in m),

B is the magnetic field strength (in T),

theta is the angle between the current and magnetic field (in degrees).

Given:

[tex]I = 850 A,\\L = 110 m,\\B = 5.00 * 10^3 T,\\\theta = 27^0[/tex]

Converting theta to radians:

[tex]\theta_{rad} = 27\degree * (pi/180) = 0.4712 rad[/tex]

Substituting the given values into the formula:

[tex]F = 850 A * 110 m * (5.00 * 10^3 T) * sin(0.4712)[/tex]

Calculating the result:

[tex]F = 850 A * 110 m * (5.00 * 10^3 T) * sin(0.4712)[/tex]

[tex]F = 34,495.88 N[/tex]

Therefore, the magnitude of the force on the 110 m section of the power line is approximately 34,495.88 N.

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The complete question is:

A DC power line for a light-rail system carries 850 A at an angle of 27° to the Earth's 5.00x 10³ T magnetic field. Randomized Variables I=850 A 1-110 m 8= 27° What is the magnitude of the force (in N) on a 110 m section of this line? F= Grade St Deduction

The magnitude of the force is 2.75 × 10⁷ N.

Given that I = 850 Aθ = 27°B = 5.00 × 10³ T

We can use the equation F = BIL sin(θ)Where F is the magnitude of the force, I is the current, L is the length of the wire, B is the magnetic field, and θ is the angle between the direction of the current and the direction of the magnetic field.

Substituting the given values into the equation above, F = (5.00 × 10³ T)(850 A)(110 m) sin(27°)F = 5.00 × 10³ × 850 × 110 × sin(27°)F = 2.75 × 10⁷ N

This rule helps to determine the direction of the magnetic force on a positive moving charge, with respect to a magnetic field. The rule states that, if we extend the fingers of our right hand perpendicular to each other, and point the thumb in the direction of the positive charge's velocity, then the direction of the magnetic force is given by the direction in which the fingers curl.

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The current across the inductor after 2 time constants will be approximately 1.948 Amperes.

To determine the current across the inductor after 2 time constants, we need to calculate the time constant and then use it to find the current at that time.

The time constant (τ) for an RL circuit can be calculated using the formula:

τ = L / R

where L is the inductance and R is the resistance.

Given that the inductance (L) is determined by the number of turns (N) and the radius of the solenoid (rsolenoid) as:

L = μ₀ * N² * A / L

where μ₀ is the permeability of free space, A is the cross-sectional area, and L is the length of the solenoid.

Calculating the inductance (L):

A = π * (rsolenoid)²

L = μ₀ * (N)² * A / L

Next, we can calculate the time constant (τ) using the resistance (R) and the inductance (L).

Using the given values:

rsolenoid = 0.0100 m

rwire = 0.00100 m

N = 60,000

Vs = 2.00 Volts

R = 0.325 Ω

After finding L and R, we can calculate τ.

Then, the current at 2 time constants (2τ) can be calculated using the equation:

I = (Vs / R) * (1 - e^{(-t/ \tow))

Substituting the values of Vs, R, and 2τ, we can find the current across the inductor after 2 time constants , Therefor the current across the inductor after 2 time constants will be 1.948 Amperes

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The kinetic energy of the asteroid just before it hits Earth is calculated as 4.27x1018 J. The speed of the asteroid just before impact is 18.4 km/s.

To calculate the kinetic energy of the asteroid just before it hits Earth, we can use the equation for kinetic energy: KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity.

Given the mass of the asteroid as 4.00x1013 kg and the velocity as 4.70 km/s, we can plug these values into the equation to find the kinetic energy just before impact, which is approximately 4.27x1018 J.

To find the speed of the asteroid just before impact, we can use the conservation of mechanical energy. The initial potential energy of the asteroid, when it is 9.0x107 km from Earth, is converted into kinetic energy just before impact. Assuming no significant energy losses due to external factors, the total mechanical energy remains constant.

The potential energy of the asteroid can be calculated using the equation PE = -GMm/r, where PE is the potential energy, G is the gravitational constant, M is the mass of Earth, m is the mass of the asteroid, and r is the distance between the asteroid and Earth.

Given the values of G, M, and r, we can solve for the potential energy and then equate it to the kinetic energy just before impact. By rearranging the equation, we can solve for the speed of the asteroid just before impact, which is approximately 18.4 km/s.

Comparing the kinetic energy of the asteroid to the output of the largest fission bomb, which is given as 2200 TJ (terajoules), we can calculate the ratio of the kinetic energy to the energy of the bomb. By dividing the kinetic energy of the asteroid by the energy of the bomb, we find that the ratio is approximately 1.94x105. This means that the kinetic energy of the asteroid is approximately 194,000 times greater than the energy released by the largest fission bomb.

This immense amount of kinetic energy, if released upon impact, would have a catastrophic impact on Earth. It would cause significant destruction, potentially leading to widespread devastation, loss of life, and changes to the Earth's geological features. The scale of such an impact would be comparable to major asteroid or meteorite impacts in the past, which have had profound effects on Earth's ecosystems and climate.

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When the kinetic energy of a moving particle decreases by 103 units due to the effect of conservative forces, then its mechanical energy will also decrease by 103 units.

Conservative forces are defined as forces that are the gradient of a scalar potential function. As a result, these forces have a unique property: they can convert mechanical energy between potential and kinetic energy and vice versa. When a particle is subjected to only conservative forces, it experiences a mechanical force that is conservative. Thus, the total mechanical energy of the particle remains constant as it moves through space.

Considering the law of conservation of energy, we have: Initial mechanical energy of the particle, Ei = Kinetic energy of the particle, Ki Final mechanical energy of the particle, Ef = Potential energy of the particle, Ui

When the kinetic energy of the moving particle decreases by 103 units, the mechanical energy of the particle also decreases by 103 units. Therefore, the new value of mechanical energy is: Ef = Ei - ΔK

Ef = Ki - ΔK

Therefore, the particle's mechanical energy will be reduced by the same amount (103 units) as its kinetic energy. Therefore, when a moving particle is subjected to conservative forces only and its kinetic energy decreases by 103 units, its mechanical energy will also decrease by 103 units.

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It will take approximately 2.747 seconds for Object B to reach Object A from the moment when Object A started to accelerate.

To find the time it takes for Object B to reach Object A, we need to consider the time it takes for Object A to reach its final velocity. Given that Object A starts from rest and has an acceleration of 1.6 m/s^2, it will take 4.0 seconds for Object A to reach its final velocity. During this time, Object A will have traveled a distance of (1/2) * (1.6 m/s^2) * (4.0 s)^2 = 12.8 meters.After the 4.0-second mark, Object B starts accelerating with an acceleration of 3.4 m/s^2. To determine the time it takes for Object B to reach Object A, we can use the equation of motion:

distance = initial velocity * time + (1/2) * acceleration * time^2

Since Object B starts from rest, the equation simplifies to:

distance = (1/2) * acceleration * time^2

Substituting the known values, we have:

12.8 meters = (1/2) * 3.4 m/s^2 * time^2

Solving for time, we find:
time^2 = (12.8 meters) / (1/2 * 3.4 m/s^2) = 7.529 seconds^2

Taking the square root of both sides, we get: time ≈ 2.747 seconds

Therefore, it will take approximately 2.747 seconds for Object B to reach Object A from the moment when Object A started to accelerate.

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velocity of approximately 8.83 x 10^10 km/year. This means that the spacecraft's velocity will be higher than the calculated average velocity by the time it reaches the distant galaxy.

According to Hubble's law, galaxies are moving away from Earth at speeds proportional to their distance. If a spacecraft is sent to a galaxy located 20 million parsecs away and it takes 7 billion years to reach its destination, we can determine its velocity.

The velocity of the spacecraft can be calculated by dividing the distance traveled by the time taken. However, since the universe is expanding, the velocity of the spacecraft will increase due to the increasing separation between galaxies.

Hubble's law states that the velocity of a galaxy moving away from Earth is directly proportional to its distance. Mathematically, this can be expressed as v = H * r, where v is the velocity of the galaxy, H is the Hubble constant (representing the rate of the universe's expansion), and r is the distance between the galaxy and Earth.

In this case, the spacecraft is traveling to a galaxy located at a distance of r = 20 million parsecs. Given that it takes 7 billion years for the spacecraft to reach its destination, we can calculate its velocity.

First, we need to convert the distance from parsecs to a more standard unit, such as kilometers. Since 1 parsec is approximately equal to 3.09 x 10^13 kilometers, the distance can be calculated as 20 million parsecs * 3.09 x 10^13 km/parsec = 6.18 x 10^20 km.

Next, we divide the distance traveled (6.18 x 10^20 km) by the time taken (7 billion years or 7 x 10^9 years) to find the average velocity of the spacecraft. This gives us a velocity of approximately 8.83 x 10^10 km/year.

However, it's important to note that the spacecraft's velocity is not constant throughout its journey. Due to the expansion of the universe, the separation between galaxies increases over time.

Therefore, as the spacecraft travels, the velocity at which the galaxy it is heading towards is moving away from Earth also increases. This means that the spacecraft's velocity will be higher than the calculated average velocity by the time it reaches the distant galaxy.

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a) W is larger than My because weight is typically greater than frictional force.

b) It depends on the specific circumstances; without more information, the nature of the collision cannot be determined.

c) The decrease in total energy does not violate the conservation of energy; energy is lost through factors like friction and deformation.

d) The calculated inertia will be larger than the actual inertia due to the error in measuring the diameter.

a) In the Friction experiment, W (weight) is larger than My (frictional force). This is because weight is the force exerted by the gravitational pull on an object, which is typically larger than the frictional force experienced by the object due to surface contact.

b) In the Collisions experiment, the nature of the collision (elastic or inelastic) would depend on the specific circumstances of the experiment. Without further information, it is not possible to determine whether the collision was elastic or inelastic.

c) In the Conservation of Energy experiment, the decrease in total energy after every bounce does not imply a violation of the conservation of energy. Some energy is lost due to factors such as friction, air resistance, and deformation of the objects involved in the experiment. This energy is usually converted into other forms such as heat or sound.

d) In the Newton's 2nd Law for Rotation experiment, if the measured diameter of the drum is larger than the actual diameter, it would result in a larger calculated value of the inertia of the system. This is because the inertia of a rotating object is directly proportional to its mass and the square of its radius. A larger measured diameter would lead to a larger calculated radius, thereby increasing the inertia value.

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(a) The electron's speed is approximately 6.37 × 10⁶ m/s.

(b) The magnetic field magnitude is approximately 2.27 × 10⁻⁴ Tesla (T).

(c) The circling frequency is approximately 2.55 × 10⁷ radians per second (rad/s).

(d) The period of the motion is approximately 3.92 × 10⁻⁸ seconds (s).

To find the electron's speed, we can use the equation:

Kinetic energy = (1/2) × m × v²

Where

Given the kinetic energy as 1.20 keV (kilo-electron volts) and the mass of an electron as approximately 9.11 × 10⁻³¹kg, we can convert the energy to joules:

1.20 keV = 1.20 × 10³ eV = 1.20 × 10³ × 1.6 × 10⁻¹⁹ J = 1.92 × 10⁻¹⁶J

Substituting the values into the equation:

1.92 × 10⁻¹⁶ J = (1/2) × (9.11 × 10⁻³¹ kg) × v²

Solving for v, we find:

v = √[(2 × 1.92 × 10⁻⁶ J) / (9.11 × 10⁻³¹kg)]

v ≈ 6.37 × 10⁶ m/s

Therefore, the electron's speed is approximately 6.37 × 10⁶ m/s.

To find the magnetic field magnitude, we can use the equation for the centripetal force:

F = (m × v²) / r

Where,

The centripetal force is provided by the magnetic force:

F = q × v × B

Where,

Setting these two expressions equal to each other and solving for B:

(q × v × B) = (m × v²) / r

B = (m × v) / (q × r)

Substituting the known values:

B = [(9.11 × 10⁻³¹kg) × (6.37 × 10⁶ m/s)] / [(1.6 × 10⁻¹⁹ C) * (0.25 m)]

B ≈ 2.27 × 10⁻⁴ T

Therefore, the magnetic field magnitude is approximately 2.27 × 10⁻⁴ Tesla (T).

The circling frequency (ω) can be calculated using the formula:

ω = v / r

Substituting the values:

ω = (6.37 × 10⁶ m/s) / (0.25 m)

ω ≈ 2.55 × 10⁷ rad/s

Therefore, the circling frequency is approximately 2.55 × 10⁷ radians per second (rad/s).

Finally, the period (T) of the motion can be calculated as the reciprocal of the circling frequency:

T = 1 / ω

T = 1 / (2.55 × 10⁷ rad/s)

T ≈ 3.92 × 10⁻⁸ s

Therefore, the period of the motion is approximately 3.92 × 10⁻⁸seconds (s).

The complete question should be:

An electron of kinetic energy 1.20keV circles in a plane perpendicular to a uniform magnetic field. The orbit radius is 25.0cm. Find

(a) the electrons speed,

(b) the magnetic field magnitude,

(c) the circling frequency, and

(d) the period of the motion.

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