Question

A conducting square loop is in a uniform magnetic field B as shown. The side length of the loop is L = 60 cm, and the loop has an effective resistance of R = 0.045 Ohm. The magnitude of B decreases steadily from an initial value B_0 = 0.050 T to zero in 0.20 seconds, and stays at zero afterwards. Find the magnitude of the induced emf in the loop. What is the current in the loop? And in what direction (briefly explain)? At what rate is energy being converted into thermal energy? Sketch the Induced emf as a function of time from 0 to 0.5 s. Briefly explain your graph. If the magnetic field 6 stays the same, should the side length L increase or decrease so as to induce the same current as in (b) above? (bonus) Find L as a function of t in order to produce a steady current as above at constant Bo. (use back of page if necessary)

Answer 1

a) magnitude of induced emf = A*dB/dt

= 0.6^2*(0.05 - 0)/0.2

= 0.09 volts

b) I = induced emf/R

= 0.09/0.045

= 2 A

Direction : clockwise

c) Rate of Thermal energy generated = I^2*R

= 2^2*0.045

= 0.18 A

d) from t = 0 to t = 0.2, emf is constnt and emf = 0.09 volts

from t = 0.2 s to 0.5 s emf = 0

e) induced emf = B*dA/dt

= B*d(L^2)/dt

induced emf = B*2*L*dL/dt

dL/dt = induced emf/(2*B*L)

= 0.09/(2*0.05*0.6)

= 1.5 m/s