The circuit in the figure below consists of switch S, a 12.0 V ideal battery, a

Question

The circuit in the figure below consists of switch S, a 12.0 V ideal battery, a 17.0 M resistor, and an air-filled capacitor. The capacitor has parallel circular plates of radius 4.00 cm, separated by 3.00 mm. At time t = 0, switch S is closed to begin charging the capacitor. Take the electric field between the plates to be uniform.

At t = 250 µs, please find:

a.) The actual current flowing to/from the capacitor plates.
____ µA

b.) The displacement current flowing between the cap plates.
0.261 µA (CORRECT)

c.) The electric field between the plates:
____   N/C

and its time rate of change at this moment:
____  (N/C)/s =  ____ (N/C)/s

d.) The size of the magnetic field:

at point 1: (outside the plates, 5 cm radially away from the midpoint of the plates):
____  T
Note that the cap's electric field dies off rapidly outside the plates. (Approximating it as an infinite cap, we say the field is zero except between the plates.)
So... does the induced magnetic field need to be inside the same region of space as the changing electric field that caused it?

at point 2: (within the plates, 3 cm radially away from the midpoint of the plates):
____  T

Explanation / Answer

C = Ae/d = A/k4*pi*d = 0.04^2/k*4*3*10^-3 = 1.48478*10^-11 F
a) I = Vb(exp(-t/RC))/R = 12(exp(-250*10^-6/17*10^6*C))/17*10^6 = 0.26217 micro A
b) Disp Current = 0.26217 micro A
c) Electric Field = V/d = 0.26217*10^(-6)*17*10^6 / 3*10^-3 = 1485.651 V/m
d) B = 2kI/r = 0.00000000000104868 T

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