Question

The potential of the electric field produced by a point charge at any point \( (x, y, z) \) is given by \( V = x^2 + 5y^2 \), where \( x \), \( y \) are in meters and \( V \) is in volts. The intensity of the electric field at \( (-2, 1, 0) \) is

• A. \( +17 \, \text{V/m} \)
• B. \( -17 \, \text{V/m} \)
• C. \( +12 \, \text{V/m} \)
• D. \( -12 \, \text{V/m} \)

Hint:

The electric field is the negative gradient of the potential.

Answer 1

The Correct Option is D

The electric field intensity is the negative gradient of the potential. We differentiate the potential with respect to \( x \), \( y \), and \( z \), then evaluate at the given point.

Step 2: Conclusion.
The intensity of the electric field at \( (-2, 1, 0) \) is \( -12 \, \text{V/m} \), corresponding to option (d).