A capacitor with circular plates of radius o.0534 m separated by a distance of 4

Question

A capacitor with circular plates of radius o.0534 m separated by a distance of 4.60 x 10-4 m is being charged by a battery with an emf of 17.0 V. A vacuum exists between the plates of the capacitor. The constructed circuit has a resistance of 400 in series with the capacitor, and the capacitor is initially uncharged when a switch is closed, completing the circuit and causing a current to flow (an RC series circuit). Find the magnitude of the magnetic field between the plates at a distance of 0.0250 m from the axis through the center of the plates, when one time constant has passed since the switch was closed

Explanation / Answer

the capacitance of the capacitor = eo*A/d

A=area, and d is the distance of separation.

so, capacitance = 8.85*10^-12*pi*0.0534^2/(4.6*10^-4)

=1.72*10^-10 F

so,

Current in the circuit is given by I = (V/R)*(1-e^t/RC)

after one time period, the current in the circuit = (V/R)*(1-e^-1)

=(17/400)*(1-1/2.71)

=0.0268 A

Also the magnetic field in a capacitor is given by the formula

B = uo*I*r/(2*pi*R^2)

where R is the radius of the capacitor and r is the distance from the axis from which magnetic field has to be found.

so,

B = 4*pi*10^-7*0.0268*0.025/(2*pi*0.0534^2)

or B = 4.7*10^-8 T

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