Assume that an electric field E=20 x^2 i exists in space. If V₀ is the potential at the origin and V_A is the potential at x=3 ~m then, the potential difference V_A-V₀ in volts is

Step-by-step solution

Concept: electric field is defined as, (- E d l )= d V Given E =20 x^2 i and d l = d x i (-20 x^2 ~d x )= d V Integrating between, x=0 to 3 ~m aligned & - ₀^3 20 x^2 ~d x= _ V₀ ^ V_A ~d V & (V_A-V₀ )=(-20) . ( x^3 3 ) |₀ ^3 ~V =(-180) V aligned