A 129 129 ‑turn circular coil of radius 2.21 cm 2.21 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 11.7 Ω 11.7 Ω resistor to create a closed circuit. During a time interval of 0.147 s, 0.147 s, the magnetic field strength decreases uniformly from 0.637 T 0.637 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.

9.11 mJ

Explanation:

Electromagnetic induction occurs when there is a change in magnetic flux linkage through a coil, and an electromotive force is induced in the coil, according to Faraday-Newmann-Lenz law:

where

N is the number of turns in the coil

is the change in magnetic flux through the coil

is the time interval

The change in magnetic flux can be rewritten as

where

is the area of the coil

is the variation of the strength of the magnetic field

So the equation becomes

here we have:

N = 129 turns

So the induced emf is

We know that the resistance of the coil is

so the current in the circuit is given by Ohm's law:

And the power dissipated through the resistor is:

And finally, the energy dissipated in the resistor in this time interval is:

conduct current i mean it makes sense