Question

A small circular washer of radius.43 cm is held directly below a long, straight wire carrying a current of 4.2 amps to the left. The washer is located 1.2 meters above the top of a table. If the washer is dropped from rest, what is the magnitude of the average induced emf in the washer and what is the direction of the induced current in the washer?

Answer 1

The magnetic field at a height h from the table

B1 = u_o I /2pi*(h + a)

where u_o is the constant of permeability

I = Current , a = radius of the washer

h = height of the washer from the table

B1 = 4pi*10^-7*4.2 / 2pi*(1.2 + 0.0043)

= 6.975*10^-7 T

Magnetic field in the washer when it reaches the table  

B2 = u_o I /2pi*a = 4pi*10^-7*4.2 / 2pi*(0.0043) = 1.95*10^-4 T

Change in flux $\Delta$ $\Phi$ = A(B2 - B1)

= pi*(0.0043)^2 * ( 1.95*10^-4 - 6.975*10^-7)

= 1.13*10^-8 Wb

h = 0.5gt^2

t = sqrt(2h/g) = sqrt(2*1.2 / 9.8) = 0.494 s

emf induced = $\Delta$ $\Phi$ / t

= 1.13*10^-8 / 0.494 = 2.28*106-8 V

direction of induced current will be determined by lenz law which states that the current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux

so the direction of current will be in clockwise direction