An ideal solenoid is 18.5 cm long, has a circular cross-section 2.20 cm in diame

Question

An ideal solenoid is 18.5 cm long, has a circular cross-section 2.20 cm in diameter, and contains 545 equally spaced thin windings. This solenoid is connected in a series circuit with an open switch, a 15.0-ohm resistor, and a battery of internal resistance 5.00 ohm and open-circuit terminal voltage of 25.0 V. (mu_0 = 4 pi times 10^-7 T middot m/A) What is the maximum amount of energy that the solenoid will store after closing the switch? How long after closing the switch will it take for the stored energy in the solenoid to reach one-half of its maximum value?

Explanation / Answer

According to the give problem,

a) First we solve for inductance, then stored energy.

L = µN2*area/length = 1.256637 *10-6 *5452 * *0.0112/0.185 = 7.669488* 10-4 H

E = LI2/2 = 7.669488*10-4 *(25/20)2/2 J

E = 5.99 *10-4 J = 0.599 mJ

b) Using the energy stored relation with time,

And substituting the values and simplifying

results in time

t = 47.1 *10-6s = 47.1 µs

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