In a certain region, the electric field is directed outward and is proportional to the distance r from the origin. Assuming the electric potential at the origin is zero, the electric potential

Step-by-step solution

Given that the electric field is directed outward and is proportional to the distance r from the origin, we can write: E = k r r where k is a positive constant. The relation between electric field and electric potential is given by: dV = - E d r Substituting the value of E : dV = -(k r r ) (dr r ) = -k r dr Integrating both sides from the origin to a distance r : ₀^ V dV = - ₀^ r k r dr V - 0 = - k r^2 2 V = - k 2 r^2 Thus, the electric potential is proportional to r^2 .