Question

An elelctric field $\overrightarrow{E}=50\hat{i}+75\hat{j}{\text{NC}}^{-1}$ exist in a certain region of space. Assume that the potential at the origin to be zero. The potential at a point $\text{P}$$(1\text{m},2\text{m})$will be

• A. $100\text{V}$
• B. $-100\text{V}$
• C. $200\text{V}$
• D. $-200\text{V}$

Answer 1

The correct option is D $-200\text{V}$

${\int }_0^{V}dV=-{\int }_0^r\overrightarrow{E}\cdot \overrightarrow{dr}=-{\int }_0^x{E}_{x}dx-{\int }_0^y{E}_{y}dy$

$V=-{\int }_0^{1}50dx-{\int }_0^{2}75dy$

$V=-[50x{]}_0^1-[75y{]}_0^2$

$=-50-150$

$=-200\text{V}$

Hence, (d) is the correct answer.