A parallel-plate air-filled capacitor is being charged as in the figure below. T
ID: 2030142 • Letter: A
Question
A parallel-plate air-filled capacitor is being charged as in the figure below. The circular plates have radius 6.00 cm, and at a particular instant the conduction current in the wires is 0.220 A 2 (a) What is the displacement current density jo in the air space between the plates? A/m2 (b) What is the rate at which the electric field between the plates is changing? V/m s (c) What is the induced magnetic field between the plates at a distance of 3.00 cm from the axis? (d) What is the induced magnetic field between the plates at 1.50 cm from the axis?Explanation / Answer
Given,
r = 6 cm ; I = 0.220 A
a)We know that
J = I/A
J = 0.220/3.14 x 0.06^2 = 19.46 A/m^2
Hence, J = 19.46 A/m^2
b)Rate at which E field changes will be
dE/dt = J/e0
dE/dt = 19.46/(8.85 x 10^-12) = 2.2 x 10^12 V/m-s
Hence, dE/dt = 2.2 x 10^12 V/m-s
c)r = 3 cm = 0.03 m
The induced B field will be given by:
B = u0 i/2 pi x r/R^2
B = 4 pi x 10^-7 x 0.220/2 pi (0.03/0.06^2) = 3.67 x 10^-7 T
Hence, B = 3.67 x 10^-7 T
d)r = 1.5 cm = 0.015 m
using the same expression:
B = 4 pi x 10^-7 x 0.220/2 pi (0.015/0.06^2) = 1.83 x 10^-7 T
Hence, B = 1.83 x 10^-7 T