Question

A 50-turn circular coil (radius = 15 cm) with a total resistance of 4.0 ohm is placed in a uniform magnetic field directed perpendicularly to the plane of the coil. The magnitude of this field varies with time according to B = A sin (at), where A = 80 mu T and alpha = 50 pi rad/s. What is the magnitude of the current induced in the coil at t = 20 ms? A long straight wire is parallel to one edge and is in the plane of a single-turn rectangular loop as shown. If the loop is changing width so that the distance x changes at a constant rate of 4.0 an/s, what is the magnitude of the emf induced in the loop at an instant when x = 6.0 cm? Let a = 2.0 cm, b = 1.2 m, and I = 30 A. A long solenoid (n = 1500 turns /m) has a cross-sectional area of 0.40 m2 and a current given by I = (4.0 + 3.0i2) A, where t is in seconds. A flat circular coil (N = 300 turns) with a cross-sectional area of 0.15 m2 is inside and coaxial with the solenoid. What is the magnitude of the emf induced in the coil at t = 2.0 s?

please show calculations. the answers are 11mA, 4.8uC, and 1.0V

Answer 1

1)

emf=d?/dt

current i=emf/R

R=4

?=N*pi*r^2*Asin(alpha*t)

N=50 r=0.15

A=80*10^-6 alpha=50 pi

d?/dt=N*pi*r^2*A*alpha*cos(alpha*t)

at t=20ms

d?/dt=50*pi*0.15*0.15*80*10^-6**50*pi*-1

=44.4132198049*10^-3

i=44.4132198049*10^-3/4

=11 mA

2)

B due to long wire at distance x is

B=