Question

In a region, the electric field is \( (30\hat{i} + 40\hat{j}) \) NC\(^{-1}\). If the electric potential at the origin is zero, the electric potential at the point (1 m, 2 m) is

• A. \( -60 V \)
• B. \( -75 V \)
• C. \( -55 V \)
• D. \( -110 V \)

Hint:

To find potential in uniform electric fields, use the path integral \( V = -\int \mathbf{E} \cdot d\mathbf{r} \).

Answer 1

The Correct Option is D

Electric potential difference is given by: \[ V = - \int \mathbf{E} \cdot d\mathbf{r} \] \[ V = - \left[ \int_{0}^{1} 30 dx + \int_{0}^{2} 40 dy \right] \] \[ = - \left[ 30(1-0) + 40(2-0) \right] \] \[ = - (30 + 80) = -110 V \] Thus, the correct answer is \( -110 V \).