SEC. 31-4 Lenz’s Law
3E. The magnetic flux through the loop shown in Fig. 31-33 increases according to the
relation ΦB = 6.0t2+7.0t, where ΦB is in milliwebers and t is in seconds. (a) What is the
magnitude of the emf induced in the loop when t = 2.0? (b) What is the direction of the
current through R?
7P. In Fig. 31-35 a 120-turn coil of radius 1.8 cm and resistance 5.3Ω is placed outside
a solenoid like that of Sample Problem 31-1. If the current in the solenoid is
changed as in that sample problem, what current appears in the coil while the
solenoid current is being changed?
15P. A square wire loop with 2.00 m sides is perpendicular to a uniform magnetic field,
with a half the area of the loop in the field as shown in Fig. 31-38. The loop contains a
20.0 V battery with negligible internal resistance. If the magnitude of the field varies with
time according to B = 0.0420 – 0.870t , with B in teslas and t in seconds, what are (a) the
net emf in the circuit and (b) the direction of the current through the battery?
17P. A rectangular coil of N turns and of length a and width b is rotated at frequency f in
a uniform magnetic field B, as indicated in Fig. 31-40. The coil is connected to corotating cylinders, against which metal brushes slide to make contact. (a) Show that the
emf induced in the coil is given (as a function of time t) by E = 2πfNabB sin (2πft) =E0
sin (2πft) = E0 = sin (2πft).
24P. A rectangular loop of wire with length a,, width b, and resistance R is placed near and infinitely long
wire carrying current I, as shown in Fig. 31-45. The distance from the long wire to the center of the loop is
r. Find (a) the magnitude of the magnetic flux through the loop and (b) the current in the loop as it moves
away from the long wire with speed v.