Question

What is displacement current? A plane electromagnetic wave of 25 MHz frequency is propagating along the x-axis in vacuum. The electric field at any point in the vacuum is \( \vec{E} = 6 \hat{j} \) volt/metre. What is the magnitude and direction of the magnetic field \( \vec{B} \) at this point?

Hint:

The magnetic field is perpendicular to both the electric field and propagation direction.

Answer 1

Displacement Current: It is the current that appears in the region where an electric field is changing with time, given by: \[ I_d = \varepsilon_0 \frac{d\Phi_E}{dt} \] Step 1: The magnitude of the magnetic field is obtained using the relation: \[ B = \frac{E}{c} \] Step 2: Substituting values: \[ B = \frac{6}{3 \times 10^8} \] \[ B = 2 \times 10^{-8} \, \text{T} \] Step 3: The direction is along the \( \hat{k} \)-axis due to cross-product rules. \[ \boxed{B = 2 \times 10^{-8} \text{ T, along } \hat{k}} \]