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=25 , C=90 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: _______ A, Direction: Counterclockwise or Clockwise?

b.) How long will it take the capacitor to charge to 25% of its final charge?

________ m/s

Which plate is positively charged? Top or Bottom?

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

________mC

Please show the work and answer for this problem. Thank You!

The magnetic field in the region shown below is increasing by 5 T/s. The circuit shown (with R=25 , C=90 Mu F, 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: _______ A, Direction: Counterclockwise or Clockwise? b.) How long will it take the capacitor to charge to 25% of its final charge? ________ m/s Which plate is positively charged? Top or Bottom? c.) How much charge will the capacitor hold after a long time (assuming this magnetic field rate increase is maintained)? ________mC Please show the work and answer for this problem. Thank You!

Explanation / Answer

a) emf = d(phi)/dt = d (AB) /dt = A dB/dt = 2 (5) = 10 V

so i = emf / R = 10 / 25 = 0.4 A

according to Lenz's law i must be Counterclockwise so that it must generate an opposite mag feld to B .

______________________________________________

b) Vc(0) = 0 , Vc(infinity) = 10 V

time constant T = RC = 2.25 ms

so Vc(t) = 10 (1 - e^-444.4t)

so Q(t) = C V = 9x10^-4 (1 - e^-444.4t)

hence 0.25 (9x10^-4) = 9x10^-4 (1 - e^-444.4t)

=> (1 - e^-444.4t) = 0.25

=> e^-444.4t = 0.75

( ln ) for both sides :

=> -444.4t = -0.288

so t = 0.647 ms

Bottom plate will be positive

______________________________________

c) after long time V = 10 V

so Q = CV = 900 x 10^-6 = 9 x 10^-4 C

=> Q = 0.9 mC

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