mEC O2

Solution

A moving electric field creates a magnetic field. This can be solved using the relation between electric and magnetic fields in a moving frame (for \(v \ll c\)) or by treating the moving surface charge as a current sheet.

Step 1: Determine Electric Field \(E\)

$$ E = \frac{V}{d} $$

Step 2: Determine Magnetic Field \(B\)

From the transformation of electromagnetic fields (or Ampere’s law considering the moving charge sheets), the magnetic field generated by an electric field \(\vec{E}\) moving with velocity \(\vec{v}\) is given by:

$$ \vec{B} = \mu_0 \epsilon_0 (\vec{v} \times \vec{E}) $$

In magnitude:

$$ B = \mu_0 \epsilon_0 v E $$

Substituting \(E = \frac{V}{d}\):

$$ B = \mu_0 \epsilon_0 v \left( \frac{V}{d} \right) = \frac{\mu_0 \epsilon_0 v V}{d} $$

Correct Answer: (a) \( \frac{\mu_0\epsilon_0 vV}{d} \)