Assume that the electric field E = 30 x^2 i exists in space. Then the potential difference V_A - V_O , where ' V_O ' is the potential at the origin and ' V_A ' is the potential at x = 2 m, is

Step-by-step solution

The relation between electric potential and electric field is given by dV = - E d r . Substituting the given electric field E = 30x^2 i and d r = dx i : dV = -(30x^2 i ) (dx i ) = -30x^2 dx Integrating both sides from the origin ( x = 0 ) to point A ( x = 2 ): _ V_O ^ V_A dV = ₀² -30x^2 dx V_A - V_O = -30 [ x^3 3 ]₀² V_A - V_O = -10 (2^3 - 0^3) V_A - V_O = -10 8 = -80 V Answer: -80 V