A200-loop coil of cross sectional area 8.5 cm2 lies in the plane of the page. an external magnetic field of 0.060 t is directed out of the plane of the page. the external field decreases to 0.020 t in 12 milliseconds. (a) what is the magnitude of the change in the external magnetic flux enclosed by the coil? (b) what is the magnitude of the average voltage induced in the coil as the external flux is changing? (c) if the coil has a resistance of 4.0 ohms, what is the magnitude of the average current in the coil?

(a) 0.0068 Wb

Since the plane of the coil is perpendicular to the magnetic field, the magnetic flux through the coil is given by

where

N = 200 is the number of loops in the coil

B is the magnetic field intensity

is the area of the coil

At the beginning, we have

so the initial magnetic flux is

at the end, we have

so the final magnetic flux is

So the magnitude of the change in the external magnetic flux through the coil is

(b) 0.567 V

The magnitude of the average voltage (emf) induced in the coil is given by Faraday-Newmann law

where

is the variation of magnetic flux

is the time interval

Substituting into the formula, we find

(c) 0.142 A

The average current in the coil can be found by using Ohm's law:

where

I is the current

V is the voltage

R is the resistance

Here we have:

V = 0.567 V (induced voltage)

(resistance of the coil)

Solving for I, we find

d eras and periods