Question

An electric field $\vec{E}=A x \hat{i}$ exists in the space, where $A=10 \,V / m ^{2}$. Consider the potential at $(10 \,m , 20\, m )$ to be zero. The potential (in $V$ ) at the origin is _______.

Answer 1

Figure shows the situation described in question. Here $B C$ is the equipotential line so we can use
$V_{C}=V_{B}=0$

If $V_{0}$ be the potential at the origin, we can use
$ V_{0}-V_{B}=\int\limits_{A}^{B} E d x=\int\limits_{0}^{10} A x d x$
$\Rightarrow V_{0}-0=A\left|\frac{x^{2}}{2}\right|_{0}^{10}=10 \times \frac{10^{2}}{2}=500 \,V$