Question

The electric field in a region is given by $\overrightarrow {E} = \left(\frac{A}{x^{3}}\right) \hat{i}$ An expression for the potential in the region assuming the potential at infinity to be zero is

• A. $\frac{A}{2x^{3}}$
• B. $\frac{2x^{3}}{A}$
• C. $\frac{A^{2}}{2x}$
• D. $\frac{A^{2}}{2x^{2}}$

Answer 1

Answer: (D)

$\frac{A^{2}}{2x^{2}}$

Answer 2

Given, $E = \frac{A}{X^3} i$
We know that,
$E = - \frac{dv}{dx}$
$\int dv = - \int - E dx$
$V = -\int(\frac{A}{x^3}) dx$
$V = \frac{1}{2} \cdot \frac{A}{x^2}$