A143 ‑turn circular coil of radius 3.43 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 10.7 ω resistor to create a closed circuit. during a time interval of 0.115 s, the magnetic field strength decreases uniformly from 0.523 t to zero. find the energy, in millijoules, that is dissipated in the resistor during this time interval.

61.9 mJ

Explanation:

We can start by calculating the emf induced in the coil by the changing magnetic field, which is given by:

where

is the change in flux linkage through the coil

is the time interval

The flux linkage through the coil is given by

where

N = 143 is the number of turns

A is the area of the coil

B is the strength of the magnetic field

The radius of the coil is

r = 3.43 cm = 0.0343 m

So its area is

So, the initial flux linkage is

where is the initial strength of the magnetic field.

The final strength of the magnetic field is zero:

So, the final flux linkage is zero:

Therefore, the change in flux linkage through the coil is

The flux linkage decreases uniformly, so the emf induced in the coil is constant and it is given by

This is also the potential difference across the resistor of the closed circuit connected to the coil, . The resistance is

So, the power dissipated through the resistor is

And therefore, the energy dissipated in the time interval of 0.115 s is

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