Consider a series circuit containing a capacitor (filled with air), a resistor a
ID: 1998484 • Letter: C
Question
Consider a series circuit containing a capacitor (filled with air), a resistor and a battery with switch. Let C = 30 pF with a circular area of 100 cm^2, V_bott = 100 V, R = 5 ohm. When the switch is closed there is an instant that the E-field between the plates is changing rapidly. Answer the following for this very brief instant. What is the "current'' between the plates, right after the switch is thrown? Include a symbolic answer and then evaluate for t ~ 0 seconds. What is the rate of change of the E-field between the plates? Include a symbolic answer and then evaluate for t ~ 0 seconds. Using Maxwell's version of Ampere's law, find an equation that describes the B- field as a function of r from the center of the circular capacitor. You may assume that E is uniform between the plates. From your answer above, where does the maximum B-field occur, and what is its value? How long does this B-field last? Roughly?Explanation / Answer
(A) at t = 0
I = 100 / 5 = 20 A
(B) I = A dE/dt
20 = (100 x 10^-4) dE/dt
dE/dt = 2000 v/ m s
(C) B (2 pi r) = u0 e0 dE/dt
B(r) = (u0 e0 dE/dt) / (2 pi r)
(D)
100 = pi r^2
r = 5.64 cm = 0.0564 m
B = (4pi x 10^-7 x 8.854 x 10^-12 x 2000) / (2 x pi x 0.0564)
B = 6.278 x 10^-14 T