Question

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

• A. $(\hat{i}+\hat{j}) V/m$
• B. $(\hat{i}-\hat{j}) V/m$
• C. $(-\hat{i}+\hat{j}) V/m$
• D. $(-\hat{i} - \hat{j}) V/m$

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 $\mathrm{E}=\left(\frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}}{\sqrt{2}}\right)$
$\mathrm{E}=\frac{\left(\mathrm{v}_{\mathrm{E}}-\mathrm{v}_{\mathrm{B}}\right)}{\mathrm{EB}}=\frac{0-(-2)}{\sqrt{2}}=\sqrt{2}$
$\therefore \overrightarrow{\mathrm{E}}=\sqrt{2} \frac{(\hat{\mathrm{i}}-\hat{\mathrm{j}})}{\sqrt{2}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$