A circular coil lies in the plane of this page and has 25 turns, a radius of 6.0

Question

A circular coil lies in the plane of this page and has 25 turns, a radius of 6.00 cm, and a total resistance of 1.80 Ohm. A magnetic field is directed into this page at an angle of 40.0 degree from the perpendicular to the plane of the coil. If the magnitude of the magnetic field varies in time according to the relationship B(t) = (50.0 mT/s^2)t^2 + (20.0 mT/s)t, then a. Find the induced current in the coil at t = 0.500 s. b. In what sense does the induced current circulate, clockwise or counterclockwise?

Explanation / Answer

a )

we have = B A cos

= 3.14 X 0.062 X cos40 X ( 50 t2 + 20 t ) X 10-3

= 8.66 X ( 50 t2 + 20 t ) X 10-3  

= - N d / dt

= - 25 X d ( 8.66 X ( 50 t2 + 20 t ) X 10-3 ) / dt

= -15.15 X 10-3 volts

= -15.15 m volts

i = / R

i = -15.15 / 1.8

i = - 8.4 mA

b )

according to Lenz's Law

the current is anticlockwise

or

counter clockwise direction.

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