Answer to Question #163851 in Electricity and Magnetism for bibo

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 a uniform magnetic field. A field of 1.5 T is directed along the positive z-direction, which is upward.

1. If the loop is removed from the field region in a time interval of 2.0ms, find the average emf that will be induced in the wire loop during the extraction process.
2. If the coil is viewed looking down on it from above, is the induced current in the loop clockwise or counterclockwise?
3. What happens to the average induced emf when the removal time is shorter?

Answer 1

1)

$\Phi_1=SB=\pi r^2 B,\\\Phi_2=0,\\\Delta\Phi=\Phi_2-\Phi_1=-\pi r^2B,$

$\xi=-\frac{\Delta\Phi}{\Delta t}=\frac{\pi r^2B}{\Delta t},$

$\xi=\frac{3.14\cdot 0.12^2\cdot 1.5}{2\cdot10^{-3}}=34 ~\text{V}.$

2)

By Lenz's law, the current has to be flaw through the loop such as to appose the removal of the magnetic field, so according to the right hand rule, the current must flow counterclockwise.

3)

$\xi \sim \frac{1}{\Delta t},$

when the removal time is shorter, the average induced emf increases.