JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
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.
- A \((-20\hat{i} + 30\hat{j})\)
- B \((20\hat{i} - 30\hat{j})\)
- C \((20\hat{i} + 45\hat{j})\)
- D \((-4\hat{i} + 6\hat{j})\)
Answer & Solution
Correct Answer
(A) \((-20\hat{i} + 30\hat{j})\)
Step-by-step Solution
Detailed explanation
The electric field \(\vec{E}\) is given by the negative gradient of the electric potential \(V\): \(\vec{E} = -\left( \dfrac{\partial V}{\partial x} \hat{i} + \dfrac{\partial V}{\partial y} \hat{j} \right)\) Given \(V = 5(x^2 - y^2)\), we find the partial derivatives:…
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