An alternating voltage source is connected in series with a 500 turn toroidal inductor and a spherical resistor. The toroidal inductor has a square profile with an inner radius of 10 cm and an outer radius of 12 cm. The resistor consists of two thin concentric spherical conducting shells with an inner radius of 2 cm an outer radius of4 cm and the space between the space if filled with a material that has a resistivity of 100 ohms cm. (a) Derive an expression for the magnetic field of the inductor and hence the induc-tance. (4 marks) (b) Derive an expression for the electric field inside the resistor and hence calculate the resistance. (4 marks) (c) Use Kirchhoff's laws to derive a relationship between the current and voltage when a voltage of Vo cos (wt) is applied to the circuit. (4 marks) Find the frequency at which the voltage drop across each component is half the total applied voltage. (3 marks)

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