Question

If uniform electric field $\vec{E}=E_{0} \hat{i}+2 E_{0} \hat{j}$, where $E_{0}$ is a constant, exists in a region of space and at $(0,0)$ the electric potential $V$ is zero, then the potential at $\left(x_{0}, 0\right)$ will be:

• A. zero
• B. $-E_{0} x_{0}$
• C. $-2 E_{0} x_{0}$
• D. $-\sqrt{5} E_{0} x_{0}$

Answer 1

Answer: (B)

$A=(0,0), \quad B=\left(x_{0}, 0\right)$
$=\int\limits_{A}^{B} \vec{E} . \,\overrightarrow{d r}=V_{A}-V_{B}=0-V_{B}$
$E_{0} x_{0}= -V_{B}$
$V_{B}=-E_{0} x_{0}$