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

ID: 2075965 • Letter: A

Question

A rod of pure silicon (resistivity =2300 m) is carrying a current. The electric field varies sinusoidally with time according to E=E0 sin t,

where E0 = 0.460 V/m , =2f, f = 113 Hz .

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

jc = A/m2

Assuming = 0, find the maximum displacement current density in the wire, and compare with the result of part A.

jD = A/m2

At what frequency f would the maximum conduction and displacement densities become equal if = 0 (which is not actually the case)?

f = Hz

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

|| =

a) Current density is given as the magnitude of the E-field over the resistivity,

J = E0/

= 0.46/2300

= 2 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*113)*0.46

= 2.89 x 10^-9 A/m^2

JD/J = 2.89e-9/2e-4 = 1.445 x 10^-5

c). We have to find f such that,

J = (2f)E0

f = J/(2E0)

= 2e-4/(2*pi*8.85e-12*0.46)

= 7.82x 10^6 Hz = 7.82 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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