Question

A circular loop of wire with a radius of 12.0 cm and oriented in the horizontal xy-plane is located in a region of uniform magnetic field. A field of 1.5 T is directed along the positive z-direction, which is upward. (a) If the loop is removed from the field region in a time interval of 2.0 ms, find the average emf that will be induced in the wire loop during the extraction process. (b) If the coil is viewed looking down on it from above, is the induced current in the loop clockwise or counter clockwise?

Short answer

1. Average emf induced will be$\epsilon =34V$
2. Induced current in the loop will be counterclockwise.

Step-by-step solution

Electric Flux

Magnetic flux is expressed as;

$\Phi =BA\cos \left(\varphi \right)$

So, here B is the magnetic field

A is area.

Average emf induced

Suppose having a circular loop of wire with radius r. It is oriented in the horizontal xy-plane and is located in a region of the uniform magnetic field with a magnitude of B=1.5T that points in the direction of the +z direction.

If the loop is removed from the field region in $∆t=2.0ms$, the magnetic field and the area initially point in the same direction, so the angle between them is $\varphi =0°$, and the initial and final fluxes are;

Here

The induced emf is equal to the flux change divided by the time it takes to go from the initial to the final flux, $∆t$, and multiplied by the number of turns N=1

So, the average emf is;

Hence, the average emf induced will be

Induced Current

According to Lenz's law, the current must flow counterclockwise through the loop to prevent the magnetic field from being removed, so the current must flow counterclockwise.

Hence, the induced current in the loop will be counterclockwise.