### RLC Circuits

A circular coil has a 10.3 cm radius and consists of 34 closely
wound turns of wire. An externally produced magnetic field of 2.62 mT is perpendicular to the coil. (a) If no current is in the
coil, what is the number of flux linkages, *N*F_{B},
for the solenoid. (b) When the current in the coil is
3.77 A in a certain direction, the net flux through the coil is found to vanish.
Find the inductance of the coil.

The inductance of a closely wound *N*-turn coil is such that an emf of 3.0 mV is induced when the current changes at the
rate of 5.0 A/s. A steady state current of 8.0 A
produces a magnetic flux of 40 mWb through each turn. (a) Calculate the inductance of the
coil. (b) How many turns does the coil have?

A toroid having a 5.20 cm square cross-section and an
inside radius of 15.3 cm has 536 turns of wire and carries a current of 810
mA. Calculate the magnetic flux through a
cross-section.