Question

In a region, uniform electric field exists as $\overrightarrow{E}=\left[10\hat{i}+10\hat{j}\right]N/C$. If the potential of origin is $0$ volts, the potential of point $(10m,10m,10m)$ is

Answer 1

$\begin{array}{c}\overrightarrow{E}=\left[10\hat{i}+10\hat{j}\right]N/C\\ V_A-V_B=\underset{A}{\overset{B}{\int }}\overrightarrow{E}.\overrightarrow{dr}\\ A\to \left(0,0,0\right)\\ B\to \left(10,10,10\right)\\ V_A=0\\ V_B=?\\ V_A-V_B=\underset{A}{\overset{B}{\int }}\left(10\hat{i}+10\hat{j}\right).\left(dx\hat{i}+dy\hat{j}+dz\hat{k}\right)\\ 0-V_B=\underset{0,0,0}{\overset{10,10,10}{\int }}\left(10dx+10dy+0dz\right)\\ -V_B={\left[10x+10y+0z\right]}_{0,0,0}^{10,10,10}\\ -V_B=10\times 10+10\times 10=-200volts\end{array}$