AIPMT PRELIMS 2009 Physics Electric Potential and Field MCQ Question
The electric potential at a point (x, y, z) is given by V = −x²y − xz³ + 4. The electric field E at that point is:
E = î 2xy + ĵ (x² + y²) + k̂ (3xz − y²)
E = î x³ + ĵ xyz + k̂ z²
E = î (2xy − z³) + ĵ x² + k̂ 3x² x
E = î (2xy + z) + ĵ x² + k̂ 3xz²
Correct Answer
Detailed Explanation
The electric field is the negative gradient of the potential, E = -∇V. Calculating the partial derivatives of V with respect to x, y, and z gives the components of E, resulting in the expression E = î 2xy + ĵ (x² + y²) + k̂ (3xz − y²).
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