Question

Write two characteristics of equipotential surfaces. A uniform electric field of 50 NC\(^{-1}\) is set up in a region along the \( x \)-axis. If the potential at the origin \( (0, 0) \) is 220 V, find the potential at a point \( (4m, 3m) \).

Hint:

The potential in a uniform electric field is a linear function of distance along the direction of the field.

Answer 1

Characteristics of Equipotential Surfaces: 1. The electric potential is the same at all points on an equipotential surface, meaning no work is done in moving a charge along the surface. 2. Equipotential surfaces are always perpendicular to the electric field lines. Since the electric field is uniform and directed along the \( x \)-axis, the potential at any point is given by: \[ V = V_0 - E \cdot d \] Where: - \( V_0 \) is the potential at the origin, - \( E \) is the magnitude of the electric field, - \( d \) is the distance along the \( x \)-axis. For the given point \( (4m, 3m) \), the distance along the \( x \)-axis is 4 m (since the electric field is along the \( x \)-axis). Therefore, the potential at this point is: \[ V = 220 \, \text{V} - 50 \, \text{NC}^{-1} \cdot 4 \, \text{m} = 220 \, \text{V} - 200 \, \text{V} = 20 \, \text{V} \] Thus, the potential at the point \( (4m, 3m) \) is 20 V.