A cylindrical solenoid with radius 1.00 cm andlength 10.0 cm consists of 300 windings of AWG 20 copper wire, whichhas a resistance per length of 0.0333 Ω/m. This solenoid is connectedin series with a 10.0 mF capacitor, which is initially uncharged. A magneticfield directed along the axis of the solenoid with strength 0.100 Tis switched on abruptly. (a) The solenoid may be considered an inductorand a resistor in series. Use Faraday’s law to determine the average emfacross the solenoid during the brief switch-on interval, and determine thenet charge initially deposited on the capacitor. (b) Attime t = 0 the capacitor is fully charged and there is no current. Howmuch time does it take for the capacitor to fully discharge the first time?(c) What is the frequency with which the current oscillates? (d) How muchenergy is stored in the capacitor at t = 0? (e) How long does it take for thetotal energy stored in the circuit to drop to 10% of that value?
A cylindrical solenoid with radius 1.00 cm and
length 10.0 cm consists of 300 windings of AWG 20 copper wire, which
has a resistance per length of 0.0333 Ω/m. This solenoid is connected
in series with a 10.0 mF capacitor, which is initially uncharged. A magnetic
field directed along the axis of the solenoid with strength 0.100 T
is switched on abruptly. (a) The solenoid may be considered an inductor
and a resistor in series. Use Faraday’s law to determine the average emf
across the solenoid during the brief switch-on interval, and determine the
net charge initially deposited on the capacitor. (b) At
time t = 0 the capacitor is fully charged and there is no current. How
much time does it take for the capacitor to fully discharge the first time?
(c) What is the frequency with which the current oscillates? (d) How much
energy is stored in the capacitor at t = 0? (e) How long does it take for the
total energy stored in the circuit to drop to 10% of that value?
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