JEE Main 2026 Apr 6 Shift 2, Physics Q12: Electric Potential

JEE Main2026Apr 6, Shift 2Physics

The electric potential as a function of $x$ , $y$ is given by $V = 5 (x^{2} - y^{2})$ V. The electric field at a point $(2, 3)$ m is ______ V/m.

Solution

Use $E = - \nabla V$ :

$E_{x} = - \frac{\partial V}{\partial x} = - 10 x$ , $E_{y} = - \frac{\partial V}{\partial y} = + 10 y$ .

At $(2, 3)$ : $E_{x} = - 20$ V/m, $E_{y} = + 30$ V/m.

$E = - 20 \hat{i} + 30 \hat{j}$ V/m.

Concept behind this question

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