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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)