The electric field in a region of space is given as $\mathbf{E}=\left(5 \mathrm{NC}^{-1}\right) x \hat{i}$. Consider point $A$ on the $Y$-axis at $y=5 \mathrm{~m}$ and point $B$ on the $X$-axis at $x=2 \mathrm{~m}$. If the potentials at points $A$ and $B$ are $V_A$ and $V_B$ respectively, then $\left(V_B-V_A\right)$ is

• A

  $-15 \mathrm{~V}$
• B

  $8 \mathrm{~V}$
• Correct answer
  C

  $-10 \mathrm{~V}$
• D

  $-12.5 \mathrm{~V}$

Solution

The given situation is shown below
Since, electric field is directed along the $X$ - axis, hence, point $A$ and $C$ lie on equipotential surface $\therefore$ Potential at point $C=$ Potential at point $A$ $\Rightarrow \quad V_C=V_A$ $\therefore \quad V_B-V_A=V_B-V_C$ $=-E \Delta x=-5(2-0)=-10 \mathrm{~V}$

Hence, the correct answer is option: 'C'.