Question

An electric field \( \vec{E} = E_0 \hat{i} \) exists in a region of space. Draw three equipotential surfaces in the region.

Hint:

For dipole-like systems at large distance: Potential falls off as \( \frac{1}{x^2} \), not \( \frac{1}{x} \).

Answer 1

Equipotential surfaces
Concept: Equipotential surfaces are always perpendicular to electric field lines.

Step 1: Direction of electric field
Given: \[ \vec{E} = E_0 \hat{i} \] So electric field is along positive x-direction.

Step 2: Nature of equipotential surfaces
Since electric field is uniform and along x-axis:
• Potential changes only along x-direction
• No change in potential along y and z directions Therefore equipotential surfaces are: \[ x = \text{constant} \]

Step 3: Final representation
Three equipotential surfaces can be represented as: \[ x = -c,\quad x = 0,\quad x = +c \] These are planes parallel to the Y–Z plane.