# A long solenoid, x, of 1000 turns and area 4× 10-3m2 carries a current of 1.2A and produces a flux density 8× 10-3 T in the middle of the coil. A small coil,Y, of 20 turns and area 2× 10-5 is placed in the middle of coil x. Find the mutual inductance, m, between the two coils.

Permeability of free space, µo= 4p × 10-7 H/m
1. (a) A 6H inductor is placed in series with a 30O resistor, an e.m.f of 8 V suddenly being applied to the combination. At 0.60 seconds after contact is made. Calculate:
(i) The rate at which energy is delivered by the battery.
(ii) The rate at which Joule heating appears in the resistor.
(iii) The rate at which energy is stored in the inductor.
(b) A long solenoid, x, of 1000 turns and area 4× 10-3m2 carries a current of 1.2A and produces a flux density 8× 10-3 T in the middle of the coil. A small coil,Y, of 20 turns and area 2× 10-5 is placed in the middle of coil x. Find the mutual inductance, m, between the two coils.

Permeability of free space, µo= 4p × 10-7 H/m
(i) Give a mathematical statement of Gauss’s law.
(ii) Determine the electric flux FE of E through a hemisphere of radius Ro given that the field is uniform and perpendicular to the axis of the hemisphere.
(iii) A conducting cylinder of radius RO and length L, and carrying charge -2q, is surrounded by a conducting cylindrical shell of radius R and charge +5q. Use Gauss’s law to find:
(a) The electric field strength at point r outside the conducting shell.
(b) The charge on the inside and outside surfaces of the conducting shell.
(c) The electric field strength in the region between the cylinders.
(iv) (i) Explain what is meant by phase of a sinusoidal alternating current.
(ii) An inductor and a capacitor are connected one at a time to a variable frequency power source. State how, and explain in non-mathematical terms why, the current through the circuit varies as the frequency varies.

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