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. Key Characteristics:

• Constant Potential: All points on an equipotential surface share the same electric potential. Consequently, no work is performed when a charge moves along such a surface.
• Perpendicular to Electric Field: Equipotential surfaces are invariably orthogonal to electric field lines. This is due to the definition of the electric field as the potential's gradient, necessitating its normal orientation to the equipotential surfaces.

2. Given Information:

• The electric field is uniform and oriented along the \( x \)-axis.
• The electric potential at any location is defined by the equation: \[ V = V_0 - E \cdot d \] where:
  • \( V_0 \) represents the potential at the origin,
  • \( E \) signifies the magnitude of the electric field,
  • \( d \) denotes the distance measured along the \( x \)-axis.

3. Calculation of Potential at \( (4m, 3m) \):

Given the electric field's alignment with the \( x \)-axis, the relevant distance \( d \) along the \( x \)-axis is 4 m. The \( y \)-coordinate of 3 m is disregarded as the field is unidirectional.

The potential at this specific point is computed using the provided formula: \[ V = 220 \, \text{V} - 50 \, \text{NC}^{-1} \cdot 4 \, \text{m} = 220 \, \text{V} - 200 \, \text{V} = 20 \, \text{V} \]

4. Conclusion:

Therefore, the electric potential at the point \( (4m, 3m) \) is determined to be \( 20 \, \text{V} \).