Question

An 8.0cm× 8.0 cm square loop is halfway into a magnetic field that is perpendicular to the plane of the loop. The loop's mass is 10 g and its resistance is 0.040 Ω . A switch is closed at t =0s, causing the magnetic field to increase from 0 to 1.0 T in 0.010 s. a) What is the induced current in the square loop? bWith what speed is the loop "kicked" away from the magnetic field? Hint: What is the impulse on the loop?

Answer 1

Area of square loop,

A = a^2 = 0.08^2

A = 0.0064 m^2

lnduced emf, e = d(BA) / dt

Since square loop is halfway into a magnetic field,

e = (A / 2)dB / dt = 0.0064 * (1 - 0) / 2*0.010

e = 0.32 V

lnduced current, I = e / R

I = 0.32 / 0.04

I = 8 A

(b)

Magnetic force, F = BIL = BIa

induced current I = e / R = (A / 2)dB / dt *R

I = (a^2 / 2)*dB / dt*R

F = B*a^3*dB / 2*dt*R

impulse = F.dt = ( B*a^3*dB / 2*dt*R) . dt

impulse = B^2*a^3 / 4R

impulse = 1*0.08^3 / 4*0.04 = 0.0032

impulse = mv = 0.0032

v = 0.0032 / 10*10^(-3)

v = 0.32 m/s