Electric field from potential – Rankers Physics
Topic: Electrostatics
Subtopic: Electric Potential

Electric field from potential

If electric potential (in volt) in a region is expressed as \(V(x, y, z) = 2xy - yz\), the electric field (in N/C) at point \((1, 0, 1)\text{ m}\) will be equal to
\(-\hat{j}\)
\(2\hat{i} - \hat{j}\)
\(-\hat{j} + \hat{k}\)
\(\hat{i} - \hat{j} + \hat{k}\)

Solution:

Using \(\vec{E} = -\left(\frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j} + \frac{\partial V}{\partial z}\hat{k}\right)\), we get \(E_x = -2y\), \(E_y = z - 2x\), and \(E_z = y\). Substituting \((1, 0, 1)\), we get \(vec{E} = -\hat{j}\).

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