The circular region with radius R = 7.35 cm shown in the figure has an electric

Question

The circular region with radius R = 7.35 cm shown in the figure has an electric field directed upwards perpendicular to the region. The amount of electric flux phi_E through a circle of radius r around the center of the region is given by the following expression: phi_E (r) = (2.65 V/s^2) times r times t^2 What is the magnitude of the displacement current at a time t = 0.335 s through the circular area with a radius r = 5.55 cm from the center of the circular region? What is the magnitude of the induced magnetic field at the same radius and time above?

Explanation / Answer

from maxwell equation

displacement current Id = e0*dphiE/dt

dphiE/dt = 2.65*r*2t = 5.3*r*t

Id = 8.85*10^-12*5.3*r*t

at time t = 0.335 s

and r = 0.055 m

Id = 8.85*10^-12*5.3*0.055*0.335 = 8.64*10^-13 A

======================

B = uo*Id/(2*r)

B = 4*pi*10^-7*8.64*10^-13/(2*0.0555)

B = 9.78*10^-18 T <<<----answer

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