# Assume that an electric field $\bar {E}=30x^2 \hat i$ 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 :

$\begin{array}{1 1}(A)\;-80\;J \\ (B)\;80\;J\\(C)\;120\;J\\(D)\;-120\;J \end{array}$

$\overrightarrow{E} = 30 x^2 \hat{i}$
$\implies dv = - \overrightarrow{E}. \overrightarrow{dx}$
\begin{align*} \int _{V_0}^{V_A} dv &= - \int_0^2 30 x^2 dx \\ & = 3 \begin{bmatrix}\frac{-x^3}{3} \end{bmatrix}^2_0 \\ & = -10 (8) J \\ &= -80 J\end{align*}
edited Nov 24, 2017