To practice problem-solving strategy 25.1 electromagnetic induction. a loop of wire of radius a = 30. mm has an electrical resistance r = 0.032 ω . the loop is initially inside a uniform magnetic field of magnitude b0 = 1.5 t parallel to the loop's axis. the magnetic field is then reduced slowly at a constant rate, which induces a current i = 0.20 a in the loop. how long does it take for the magnitude of the uniform magnetic field to drop from 1.5 t to zero? as the external magnetic field decreases, an induced current flows in the coil. what is the direction of the induced magnetic field caused by this current?

1. 0.66 s

The current induced in the loop is

I = 0.20 A

while the resistance of the loop is

so the emf induced in the loop can be found by using Ohm's law

We also know that according to Faraday-Newmann-Lenz, the induced emf is

(1)

where

is the variation of magnetic flux through the loop

is the time interval

We have:

- Initial magnetic field: B = 1.5 T

- Radius of the coil: r = 30 mm = 0.03 m

- So, area of the coil:

so the initial flux through the coil is

While the final flux through the coil is zero, since the magnetic field at the end is zero, so the change in magnetic flux is

Now re-arranging eq.(1) we find the time interval needed:

2. Same direction as the external magnetic field

The direction of the induced magnetic field is given by Lenz's law.

In fact, Lenz law states that the induced current in the loop is such that the magnetic field opposes the variation of magnetic flux through the coil.

Here, the magnetic flux through the coil is decreasing, since the external magnetic field is decreasing: this means that the induced magnetic field must be in the same direction as the external magnetic field (in order to restore the flux and to oppose this decrease of flux).