Question

The displacement current due to time varying electric field is given by

• A. \(\mu_0 \frac{d\phi_E}{dt}\)
• B. \(\epsilon_0 \frac{d\phi_E}{dt}\)
• C. \(\mu_0 \epsilon_0 \frac{d\phi_E}{dt}\)
• D. \(\frac{d\phi_E}{dt}\)

Hint:

Displacement current is crucial in Maxwell's equations to ensure that the equation is consistent in both electric and magnetic fields, particularly when there is a time-varying electric field.

Answer 1

The Correct Option is C

The displacement current is a quantity that appears in Maxwell's equations. It is proportional to the rate of change of the electric flux \(\phi_E\). The general form of the displacement current is: \[ I_d = \mu_0 \epsilon_0 \frac{d\phi_E}{dt} \] where \(\mu_0\) is the permeability of free space, \(\epsilon_0\) is the permittivity of free space, and \(\frac{d\phi_E}{dt}\) is the time rate of change of the electric flux. Thus, the correct option is: \[ \mu_0 \epsilon_0 \frac{d\phi_E}{dt} \]