Question

The electric field in a region is given by $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)

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