Electric field in a region is given by E = Axi + Byj where A = 10 V/m² and B = 5 V/m². If electric potential at point (10,20) is 500 V, find electric potential at origin.

Solution:

Given electric field:

E = Axi + Byj

A = 10 V/m², B = 5 V/m²

Relation between electric field and potential:

E = -∇V

So,

∂V/∂x = -Ax

∂V/∂y = -By

Integrating:

V = -(A/2)x² -(B/2)y² + C

Substitute values:

V = -5x² -2.5y² + C

Given:

At (10,20), V = 500 V

500 = -5(10²) -2.5(20²) + C

500 = -500 -1000 + C

C = 2000

At origin (0,0):

V = 2000 V

Answer: 2000 V