• A circular conducting loop with radius a and resistance R2 is concentric with a circular conducting loop with radius b » a (b much greater than a) and resistance R1. A time-dependent voltage is applied to the larger loop, having a slow sinusoidal variation in time given by V(t) = V0 sin ωt, where V0 and ω are constants with dimensions of voltage and inverse time, respectively. Assuming that the magnetic field throughout the inner loop is uniform (constant in space) and equal to the field at the center of the loop, derive expressions for the potential difference induced in the inner loop and the current i through that loop. (Use the following as necessary: a, b, R1, R2, V0, ω, t, and μ0.)

• The conducting loop in the shape of a quartercircle shown in the figure has a radius of 20 cm and resistance of 0.8 Ω. The magnetic field strength within the dotted circle of radius 6 cm is initially 5 T. The magnetic field strength then decreases from 5 T to 1 T in 7 s. (a) Find the magnitude of the induced current in the loop. (b) Find the direction of the induced current in the loop.

• A short coil with radius R = 18 cm contains N = 30 turns and surrounds a long solenoid with radius r = 3.0 cm containing n = 60 turns per centimeter. The current in the short coil is increased at a constant rate from zero to i = 1.5 A in a time of t = 16 s. Calculate the induced potential difference in the long solenoid while the current is increasing in the short coil.
• In the circuit in the figure, a battery supplies Vemf = 10 V and R1 = 4.0 Ω, R2 = 4.0 Ω, and L = 2.0 H. Calculate each of the following a long time after the switch is closed. (a) the current flowing out of the battery. (b) the current through R1; (c) the current through R2; (d) the potential difference across R1; (e) the potential difference across R2; (f) the potential difference across L; (g) the rate of current change across R1.

• An emf of 30 V is applied to a coil with an inductance of 34 mH and a resistance of 0.70 Ω. (a) Determine the energy stored in the magnetic field when the current reaches one fourth of its maximum value. (b) How long does it take for the current to reach this value?

Q. An emf of 24.0 V is applied to a coil with an inductance of 58.0 mH and a resistance of 0.41 Ω.

a) Determine the energy stored in the magnetic field when the current reaches one fourth of its maximum value.

b) How long does it take for the current to reach this value?

Answer:  a)The maximum current, after a long time has elapsed, will be 24/0.41 = 58.5A. A quarter of this is 14.63A. Energy stored in an inductor is 0.5*L*I^2 = 6.21J

b) you can use I(t)/ Imax =1 - exp(-t*R/L) where I(t) is the current at time t (14.63A), Imax is the maximum current (58.5A), R is the resistance, L the inductance

0.75 = exp(-t*7.07)

t*7.07= 0.288

t = 40.7ms

• A motor has a single loop inside a magnetic field of magnitude 0.95 T. If the area of the loop is 200. cm2, find the maximum angular speed possible for this motor when connected to a source of emf providing 210 V.