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, then the electric potential at origin is \_\_\_\_ V.

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Quantrex Academy · Accepted Answer

Correct answer: B. 2000

The electric field is related to potential by

\vec{E} = -\nabla V

.
Given:

\vec{E} = Ax\hat{i} + By\hat{j}

with

A = 10

V/m² and

B = 5

V/m²
This means:

\frac{\partial V}{\partial x} = -Ax

and

\frac{\partial V}{\partial y} = -By

Integrating:

V(x,y) = -\frac{Ax^2}{2} - \frac{By^2}{2} + C = -5x^2 - \frac{5y^2}{2} + C

Using the boundary condition at

(10, 20)

where

V = 500

V:

500 = -5(100) - \frac{5(400)}{2} + C

500 = -500 - 1000 + C

C = 2000

V
At the origin

(0, 0)

:

V(0,0) = -5(0) - \frac{5(0)}{2} + 2000 = 2000

V

Electric field in a region is given by E =A x i +B y j , where A=10...

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