Question

A positive charge q is carried from a point x to y in an electric field of point charge Q. the work done by the field in SI unit is

• A. $\frac{qQ}{4\pi {ϵ}_0}[\frac{1}{b^2}-\frac{1}{a^2}]$
• B. $\frac{qQ}{4\pi {ϵ}_0}[\frac{1}{a}-\frac{1}{b}]$
• C. $\frac{qQ}{4\pi {ϵ}_0}[\frac{1}{a}+\frac{1}{b}]$
• D. $\frac{qQ}{4\pi {ϵ}_0}[\frac{1}{a^2}-\frac{1}{b^2}]$

Answer 1

The correct option is B $\frac{qQ}{4\pi {ϵ}_0}[\frac{1}{a}-\frac{1}{b}]$

As we know,

Using, $E=-\frac{dV}{dx}$, we get, $dV=-E.dx$ or $dV=-\frac{1}{4\pi {ϵ}_0}\frac{q}{x^2}dx$

$\therefore V=-\frac{1}{4\pi {ϵ}_0}\frac{q}{x^2}dx=\frac{q}{4\pi {ϵ}_0}{\left[\frac{1}{x}\right]}_b^a=\frac{q}{4\pi {ϵ}_0}[\frac{1}{a}-\frac{1}{b}]$

or $W=QV=\frac{qQ}{4\pi {ϵ}_0}[\frac{1}{a}-\frac{1}{b}]$