# Physics

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A solenoid has N=1568.0 turns, length d=32 cm , and radius b=0.2 cm, (b<<d) . The solenoid is connected via a switch, S1 , to an ideal voltage source with electromotive force ϵ=13 V and a resistor with resistance R=25 Ohm . Assume all the self-inductance in the circuit is due to the solenoid. At time t=0 , S1 is closed while S2 remains open.

(a) Fig. 1

(b) Fig. 2
(a) When a current I=0.260 A is flowing through the outer loop of the circuit (i.e. S1 is still closed and S2 is still open), what is the magnitude of the magnetic field inside the solenoid (in Tesla)?

(b) What is the self-inductance L of the solenoid (in H)?

(c) What is the current (in A) in the circuit a very long time (t>>L/R) after S1 is closed? .

(d) How much energy (in J) is stored in the magnetic field of the coil a very long time (t>>L/R) after S1 is closed?

For the next part, assume that a very long time (t>>L/R) after the switch S1 was closed, the voltage source is disconnected from the circuit by opening switch S1. Simultaneously, the solenoid is connected to a capacitor of capacitance C=151 μF by closing switch S2. Assume there is negligible resistance in this new circuit.

(e) What is the maximum amount of charge (in Coulombs) that will appear on the capacitor?

(f) How long does it take (in s) after S1 is opened and S2 is closed before the capacitor first reaches its maximum charge?

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