Electric field in a region is given by E ⃗ \vec{E} E = Axî + Byĵ, where A = 10 V/m² and B = 5 V/m². If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin i s ______ V.
Physics · Electrostatics · potential energy and electric potential
JEE Mains 2026 22 January Morning Shift

Question

Electric field in a region is given by E ⃗ \vec{E} E = Axî + Byĵ, where A = 10 V/m² and B = 5 V/m². If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin i s ______ V.

Physics · Electrostatics · potential energy and electric potential

JEE Mains 2026 22 January Morning Shift

G1 Physics · Accepted Answer

The electric field is related to potential by E⃗ = -∇V. Therefore, dV = -E⃗·dr⃗. Here, E⃗ = 10xî + 5yĵ. Move from the origin to the point (10, 20): V(10,20) - V(0,0) = -∫[10x dx + 5y dy]. Therefore, 500 - V(0,0) = -[5x² + (5/2)y²] evaluated from (0,0) to (10,20). Thus, 500 - V(0,0) = -[5(10)² + (5/2)(20)²] = -[500 + 1000] = -1500. Hence, V(0,0) = 500 + 1500 = 2000 V. Correct option: C.