Question

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

• A. 21 kV
• B. -21 kV
• C. 39 kV
• D. - 39 kV

Answer 1

Answer: (B)

Here, $\vec{E}=(5 \hat{i}-3 \hat{j}) \,g \,V / m$
$V_{B}=V_{A}=-\int\limits_{r_{A}}^{r_{B}}$
$=-\int\limits_{(10,3,0)}^{(4,0,3)}(5 \hat{i}-3 \hat{j}) \cdot(d x \hat{i}+d y \hat{j}+d z \hat{k})$
$=-5(10-4)+3(3-0)$
$=-30+9$
$=-21\, k V$