jangyasinniTeacher
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To find the frequency at which the conduction current ((I_c)) and displacement current ((I_d)) become equal in a material, we first need to understand the equations governing these currents in relation to the material’s properties.
The conduction current density ((J_c)) is given by Ohm’s law:
[J_c = sigma E]
where (sigma) is the conductivity of the material and (E) is the electric field.
The displacement current density ((J_d)) can be described in relation to the changing electric field as:
[J_d = epsilon frac{dE}{dt}]
where (epsilon) is the permittivity of the material, and (frac{dE}{dt}) represents the rate of change of the electric field with respect to time.
Given that (sigma = 1) S/m (unity conductivity) and (epsilon = 2), to find the frequency ((f)) at which (J_c = J_d), set the expressions for (J_c) and (J_d) equal to each other and solve for (f).
[J_c = J_d]
[sigma E = epsilon frac{dE}{dt}]
Because we’re concerned with frequencies, a useful form of (E) to consider is one that oscillates sinusoidally, so let (E = E_0 sin(
b
Explanation: When Jd = Jc , we get εωE = σE. Thus εo(2∏f) = σ. On substituting
conductivity as one and permittivity as 2, we get f = 9GHz
b) 9 GHz
Explanation: When Jd = Jc , we get εωE = σE. Thus εo(2∏f) = σ. On substituting
conductivity as one and permittivity as 2, we get f = 9GHz.