The magnetic field in the region shown below is increasing by 5 T/s. The circuit

Question

The magnetic field in the region shown below is increasing by 5 T/s. The circuit shown (with R=20 , C=70 µF, dimensions 1 m by 2 m) is inserted into the region as shown. The capacitor is initially uncharged.

a.) What is the current in the circuit at the moment the circuit is put in the B field?
size: .5 A
direction:counterclockwise

b.) How long will it take the capacitor to charge to 25% of its final charge?
  and which plate will be positively charged?

???

c.) How much charge will the capacitor hold after a long time (assuming this magnetic field rate increase is maintained)?
.7 mC

Explanation / Answer

here,

B = 5 T/s

area = 2 m^2

emf = B*area*cos(theta) /time

EMF = 5 * 2

EMF = 10 V

a)

resistance , r = 20 ohm

C = 70 * 10^-6 F

the current in the circuit at the moment the circuit is put in the B field , I = EMF/r

EMF = 0.5 A

b)

charge , Q = Q0 * ( 1 - e^-t/T)

here , Q = 0.25 Q0

T = R*C

T = 0.0014 s

then

0.25 * Q0 = Q0 * ( 1 - e^-t/0.0014)

t = 4.03 * 10^4 s

the time taken is 4.03 * 10^4 s

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