Question Detail
Question
The potential of a charge in two dimension is given as V(x,y) = 3x + 4y. Determine the electric field intensity of the charge in V/m.
Correct Answer
Option C is the correct answer.
Detailed Explanation
The electric field intensity E is the negative gradient of the electric potential V, given by E = -∇V = -(∂V/∂x î + ∂V/∂y ĵ).Given V(x,y) = 3x + 4y:∂V/∂x = 3∂V/∂y = 4So, E = -(3î + 4ĵ).The magnitude of the electric field is |E| = √((-3)² + (-4)²) = √(9 + 16) = √25 = 5 V/m.
Hint
Remember that the electric field is the negative gradient of the electric potential. Calculate the partial derivatives and then find the magnitude of the resulting vector.