Q. The electric potential at a point (x, y, z) is given by V = −x²y − xz³ + 4. The electric field E⃗ at that point is:
A) E⃗ = î 2xy + ĵ(x² + y²) + k̂(3xz − y²)
B) E⃗ = î z³ + ĵ xyz + k̂ z²
C) E⃗ = î(2xy − z³) + ĵ xy² + k̂ 3z²x
D) E⃗ = î(2xy + z³) + ĵ x² + k̂ 3xz²
Explanation
[Solution from source] E⃗ = −∇V. −∂V/∂x = 2xy + z³, −∂V/∂y = x², −∂V/∂z = 3xz². So E⃗ = î(2xy + z³) + ĵx² + k̂3xz². A sign slip on the z³ term gives the (2xy − z³) form. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.