Question

An electric field is given by $E_{x}=-2 x^{3} \hat{i} N / C$. The potential of the point $(1,-2)$, if potential of the point $(2,4)$ is taken as zero, is

• A. $-7.5 \times 10^{3} V$
• B. $7.5 \times 10^{3} V$
• C. $-15 \times 10^{3} V$
• D. $15 \times 10^{3} V$

Answer 1

Answer: (A)

$d V=-\vec{E} \cdot d \vec{r}=-\left(-2 x^{3} \hat{i}\right) \cdot(d x \hat{i}+d y \hat{j}+d z \hat{k})$
$=2 x^{3} d x$
$\Rightarrow \int\limits_{0}^{V} d V=\int\limits_{2}^{1}\left(2 x^{3}\right) \times 10^{3} d x$
$V= -7.5 \times 10^{3} V$