A rod of pure silicon (resistivity=2300 *m ) is carrying a current. The electric

Question

A rod of pure silicon (resistivity=2300 *m ) is carrying a current. The electric field varies sinusoidally with time according to E=E0 sint where E0=0.410 V/m, =2f, f=120 Hz.

Part A:

Find the magnitude of the maximum conduction current density in the wire.

jc= (A/m2)

Part B:

jD= (A/m2)

Part C:

f= (Hz)

Part D:

At the frequency determined in part C, what is the relative phase of the conduction and displacement currents?

= (degrees)

I apologize for so many parts. Any help would be appreciated, I feel that with explanation to A&B, I might can do C&D. Will rate lifesaver if you can help me!

Explanation / Answer

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A. Current density is given as the magnitude of the E-field over the resistivity,

J = E0/ = 0.41/2300 = 1.78 x 10^-4 A/m^2

B. For an isotropic dielectric case the displacement current density is,

JD = *d/dt(E) = d/dt(E0*sin(t)) = E0*cos(t)

the magnitude of JD = |JD| = E0 = 8.85e-12*2*120*0.41 = 2.74 x 10^-9 A/m^2

JD/J = 2.74e-9/1.78e-4 = 1.54 x 10^-5

C. We have to find f such that,

J = (2f)E0

f = J/(2E0) = 1.78e-4/(2*pi*8.85e-12*0.41) = 7.81 x 10^6 Hz = 7.81 MHz

D. J = E0/*sin(t) and JD = E0*cos(t) = E0*sin(/2-t)

The phase different is,

= /2 radians = 90 degrees

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