A circular capacitor has a radius R = 0 . 200 m as shown in the figure. The elec

Question

A circular capacitor has a radius R = 0.200 m as shown in the figure. The electric field between the plates is given by Ey = 1.50 t2 N/(Cs2), where the time t is in seconds.

a) As a function of time, what is the magnitude of the magnetic field between the plates a

distance r = 0.120 m from the axis of the circular plates?

b) As a function of time, what is the magnitude of the magnetic field between the plates a

distance r = 0.240 m from the axis of the circular plates?

c) As a function of time, what is the total displacement current through the capacitor?

Explanation / Answer

a) As a function of time, what is the magnitude of the magnetic field between the plates a distance r = 0.120 m from the axis of the circular plates? we have B*2pi*R=E*S*muy0*epsilon0. so B=1.5*t2*pi*R^2*muy0*epsilon0=B*2pi*R. so 0.75*t^2*R*muy0*epsilon0=B=1e-18t^2 b) As a function of time, what is the magnitude of the magnetic field between the plates a distance r = 0.240 m from the axis of the circular plates? We have B*2pi*r=E*S0*muy0*epsilon0. where S0=pi*R0^2 (R0=0.2m). = pi*0.04. so B*2*pi*0.24=1.5*t^2*pi*0.04*muy0*epsilon0 so B=0.75*t^2*(1/6)*muy0*epsilon0=1.4e-18t^2 c) As a function of time, what is the total displacement current through the capacitor? I=epsilon0*E*S0=1.67e-12t^2(A)

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