Electric field in a region is given by E=A x i+B y j, where A=10 ~V / m^2 and B=5 ~V / m^2. If the electric potential at a point (10,20) is 500 V,…
JEE Main 2026 — Physics Electromagnetism
2026mcqmedium
Electric field in a region is given by E=Axi^+Byj^, where A=10V/m2 and B=5V/m2. If the electric potential at a point (10,20) is 500 V, then the electric potential at origin is ____ V.
Official previous-year question
Held on 22 Jan 2026 · Verified 6 Jul 2026.
Options
A
0
B
2000
C
500
D
1000
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Solution
The electric field is related to potential by E=−∇V.
Given: E=Axi^+Byj^ with A=10 V/m² and B=5 V/m²
This means:
∂x∂V=−Ax and ∂y∂V=−By
Integrating:
V(x,y)=−2Ax2−2By2+C=−5x2−25y2+C
Using the boundary condition at (10,20) where V=500 V:
500=−5(100)−25(400)+C
500=−500−1000+C
C=2000 V
At the origin (0,0):
V(0,0)=−5(0)−25(0)+2000=2000 V
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