# Assume that an electric field $\;\overline{E} =30x^{2} \hat{i}\;$ exists in space .Then the potential difference $\;V_{A}-V_{O}\;$ , where $\;V_{O}\;$ is the potential at the origin and $\;V_{A}\;$ the potential at x=2 m is :

$(a)\;120\;J \qquad(b)\;-120\;J\qquad(c)\;-80\;J\qquad(d)\;80\;J$

The correct answer is (c) - 80 V As we know, - dV/dr=E Integration dV = integration E. dr V= - integration 30x^2 V= - 10x^3 At O, x=0 Vo=0V At A, x=2 Va=-80 V Hence, Va-Vo= - 80 V