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A solid metal cube of edge length 2 cm is moving in the positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis is :
  • a)
    6 mV
  • b)
    1 mV
  • c)
    12 mV
  • d)
    2 mV
Correct answer is option 'C'. Can you explain this answer?
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A solid metal cube of edge length 2 cm is moving in the positive y-dir...
Given:
- Edge length of the cube = 2 cm = 0.02 m
- Speed of the cube in the positive y-direction = 6 m/s
- Magnetic field in the positive z-direction = 0.1 T

To find: The potential difference between the two faces of the cube perpendicular to the x-axis

The potential difference between two points in an electric field can be calculated using the formula:
ΔV = E * d

Where:
ΔV is the potential difference
E is the electric field strength
d is the distance between the two points

In this case, the cube is moving in the y-direction, so the electric field is induced due to the magnetic field (Faraday's law of electromagnetic induction).

1. Calculate the induced electric field:
The induced electric field (E) can be calculated using the formula:
E = v * B

Where:
E is the induced electric field
v is the velocity of the cube
B is the magnetic field strength

Substituting the given values:
E = 6 m/s * 0.1 T
E = 0.6 V/m

2. Calculate the distance between the two faces perpendicular to the x-axis:
The distance between the two faces perpendicular to the x-axis is equal to the edge length of the cube, which is 0.02 m.

3. Calculate the potential difference:
Using the formula ΔV = E * d, we can calculate the potential difference:
ΔV = 0.6 V/m * 0.02 m
ΔV = 0.012 V = 12 mV

Therefore, the potential difference between the two faces of the cube perpendicular to the x-axis is 12 mV, which corresponds to option C.
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A solid metal cube of edge length 2 cm is moving in the positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis is :a)6 mVb)1 mVc)12 mVd)2 mVCorrect answer is option 'C'. Can you explain this answer?
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