The magnetic field in the region shown below is increasing by 5 T/s. The circuit
ID: 2262583 • Letter: T
Question
The magnetic field in the region shown below is increasing by 5 T/s. The circuit shown (with R=30 ohm, C=75 mu F, dimensions 1 m by 2 m) is inserted into the region as shown. The capacitor is initially uncharged. What is the current in the circuit at the moment the circuit is put in the B field? size: direction: counter clockwise How long will it take the capacitor to charge to 25% of its final charge? and which plate will be positively charged? Bottom How much charge will the capacitor hold after a long time (assuming this magnetic field rate increase is maintained)?Explanation / Answer
The voltage induced in the loop is E=NAdB/dt=1*2*5=10 volts.
a) The initial current will be 10/30=.333 amps.
c) 10 volts. Q=CV
so Q=7.5X10^-6X10=0.75mc
b)
Q(t)=Qf(1-e^t/rc)
using Q=VC
V=IR so,
Q=IRC=(0.33)(30)(7.5)x10^-6
Qf=7.425x10^-6
Q(t)=Qf(1-e^t/rc)
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