Consider the magnitudes and directions of the induced potential difference in the following situations:

(a) A current-carrying straight wire moving with a speed of 1.5" " m/s towards a stationary coil.

(b) The same current-carrying straight wire moving away with a speed of 1.5" " m/s from the same stationary coil.

The induced potential differences are of magnitude(s) and have sign⁡(s) in the above two cases.

Correct option is C

The correct answer is (C) Different, Opposite

To analyze the situation and determine the induced potential difference in both cases, we can apply Faraday's Law of Induction, which states:

​$$\text{Induced EMF} = -\frac{d\Phi_B}{dt}$$ ​

Situation A: Wire moving towards the stationary coil

• As the current-carrying wire moves towards the stationary coil, the magnetic flux through the coil increases.
• According to Lenz's Law, the induced EMF will oppose this change, which means the induced current will try to create a magnetic field that opposes the increase in flux.
• The direction of the induced potential difference will be determined by the direction of this opposing current.

Situation B: Wire moving away from the stationary coil

• As the wire moves away, the magnetic flux through the coil decreases.
• Again, by Lenz's Law, the induced EMF will oppose the decrease in flux, so the induced current will try to maintain the original magnetic flux.
• The direction of the induced potential difference will be opposite to the direction in situation A because the induced current opposes the flux decrease rather than the flux increase.

Conclusion:

• The magnitudes of the induced potential differences will be the same because the relative speed of the wire is the same (1.5 m/s) in both cases.
• The directions of the induced potential differences will be opposite because the wire is moving towards the coil in the first case and away from it in the second case, resulting in opposite changes in the magnetic flux.