A rectangular metal loop with 0.045 ? resistance is placed next to one wire of t

Question

A rectangular metal loop with 0.045 ? resistance is placed next to one wire of the RC circuit shown in the figure below. The capacitor is charged to 20 V with the polarity shown, then the switch is closed at

A rectangular metal loop with 0.045 ?resistance is placed next to one wire of the RC circuit shown in the figure below. The capacitor is charged to 20 V with the polarity shown, then the switch is closed at What is the current in the loop at t = 5.2 ?s? Assume that only the circuit wire next to the loop is close enough to produce a significant magnetic field. (Use 4? ? 10?7 T m/A for the permeability constant ?0.)

Explanation / Answer

a) current direction is from positive plate to negative plate
b)Given that the potential difference is V=20V
the capacitance is C=5 x 10-6 F
resistance is R=2?
then the current at t=0 is
i0=V/R
=10A
the time constant is T=RC=10-5 s
then the current at time t= 5.2 x 10-6 sec is
i=i0 x e-t/T
=10 e -0.5
=5.9452054797A
the area of the loop is A=2 x 10-4 m 2
magnetic field at a distance 0.5cm is
B1=?i/2?d1
=2.424 x 10-4
magnetic field at a distance 1.5cm is
B2=?i/2?d2
=0.808 x 10-4
so the change in magnetic field is dB=1.616x 10-4
hence the induced emf in the circuit is E=A dB/T
=2 x 10-4 x 1.616 x 10^-4/10^-5
=2.65 x 10^-5
hence the current in the loop is I=
E/R
=2.65 x 10^-5/0.045
=0.5889 mA

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