Question

The grid represents a region in space containing a uniform electric field $($ each square of size $1m\times 1m$ . If potentials at point $\text{O}$ , $\text{A}$ , $\text{B}$ , $\text{C}$ , $\text{D}$ , $\text{E}$ , $\text{F}$ , $\text{G}$ , $\text{H}$ are respectively $\text{0}$ , $-\text{1}$ , $-\text{2}$ , $\text{1}$ , $\text{2}$ , $\text{0}$ , $-\text{1}$ , $1$ and $0$ volts. find the electric field intensity.

• A. $\left(\hat{i}+\hat{j}\right){\left(\text{V m}\right)}^{-1}$
• B. $\frac{\left(\hat{i}-\hat{j}\right)}{2}{\left(\text{V m}\right)}^{-1}$
• C. $\left(-\hat{i}+\hat{j}\right){\left(\text{V m}\right)}^{-1}$
• D. $\left(\frac{-\hat{i}+\hat{j}}{2}\right){\left(\text{V m}\right)}^{-1}$

Answer 1

Answer: (B)

OEH is an equipotential surface, the uniform electric field must be perpendicular to it pointing from higher to lower potential as shown.


Hence $\hat{E}=(\frac{\hat{i}-\hat{j}}{\sqrt{2}})$
$\left|E\right|=\frac{(v_E-v_B)}{EB}=\frac{0-(-1)}{\sqrt{2}}=\frac{1}{\sqrt{2}}$
$\Rightarrow \vec{E}=\left|E\right|\hat{E}=\frac{1}{\sqrt{2}}\left(\frac{\hat{i}-\hat{j}}{\sqrt{2}}\right)=\frac{\hat{i}-\hat{j}}{2}{\left(\text{V m}\right)}^{-1}$