Question

The electric field in a certain region is given by, $\overrightarrow{E}=\left(5\hat{i}\right)\text{kV/m}$. The potential difference $(V_B-V_A)$ between two points $A$ and $B$ having co-ordinates $(4,0,0)$ and $(10,3,0)$ respectively, is equal to -

$($co-ordinates $x,y$ and $z$ are in metre$)$

• A. $12\text{kV}$
• B. $18\text{kV}$
• C. $-42\text{kV}$
• D. $-30\text{kV}$

Answer 1

The correct option is D $-30\text{kV}$

The relation between electric field and potential difference is given by,

$V_B-V_A=-{\int }_{r_A}^{r_B}\overrightarrow{E}.\overrightarrow{dr}$

$\Rightarrow V_B-V_A=-{\int }_{4,0,0}^{10,3,0}\left(5000\hat{i}\right).(dx\hat{i}+dy\hat{j}+dz\hat{k}$

$\Rightarrow V_B-V_A=-{\int }_{4,0,0}^{10,3,0}5000dx=-5000{\left[x\right]}_4^{10}$

$=–5000[10–4]=–30\text{kV}$