Question

A conducting wire sits on smooth metal rails as shown in figure. A variable magnetic field points out of the page. The strength of this magnetic field is increased linearly from zero. Immediately after the field starts to increase, what will be the direction of the current in the wire and the direction of the wires motion?

• A. South to North; No-motion
• B. North to South; towards West
• C. South to North; towards West
• D. South to North; towards East

Answer 1

Answer: (B)

North to South; towards West

By Lenz's Law, current will flow in the wire to oppose the cause. As magnetic field is increasing, the current in the loop will flow such that the flux due to the induced current in the coil opposes the increase in external magnetic field or magnetic field due to the induced current will be inside the page. Hence, current will flow clockwise. In the wire, this implies a current from North to South.

Now, this acts like a current carrying wire placed in magnetic field. By Lorentz force, the force acting on the wire is given by:

$\overrightarrow{F}=I(\overrightarrow{L}\times \overrightarrow{B})$

$=ILB(-\hat{j}\times \hat{k})$

$=-ILB\hat{i}$

Hence, force acting on the wire is from west to east.