An electric field given by E = i Ax is present in a region of space, where A = 10 V m ⁻² . If the potential at (10 m , 20 m ) is assumed to be zero, calculate the potential at the origin.

Step-by-step solution

The relation between electric field and potential is given by dV = - E d r . Given E = A x i , we have: dV = -(A x i ) (dx i + dy j + dz k ) = -A x dx Integrating both sides from the reference point (10, 20) to the origin (0, 0) : _ V(10, 20) ^ V(0, 0) dV = - ₁₀⁰ A x dx V(0, 0) - V(10, 20) = -A [ x^2 2 ]₁₀⁰ Substituting V(10, 20) = 0 and A = 10 V m ⁻² : V(0, 0) - 0 = -10 ( 0 - 10^2 2 ) V(0, 0) = -10 (-50) = 500 V