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If \(\mathbf{E}=-(2y^3-3yz^2)\hat{x}-(6xy^2-3xz^2)\hat{y}+(6xyz)\hat{z}\) is the electric field in a source-free region, a valid expression for the electrostatic potential is
- xy^3-yz^2
- 2xy^3-xyz^2
- y^3+xyz^2
- 2xy^3-3xyz^2
Correct answer: 2xy^3-3xyz^2
Solution
In electrostatics, \(\mathbf{E}=-\nabla V\). So we need a potential whose partial derivatives match the given field components with a minus sign. Differentiating \(V=2xy^3-3xyz^2\) gives the required \(x\), \(y\), and \(z\) components.
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