Question

An infinite line charge of uniform linear charge density $\lambda$ is placed along the $z$-axis. The work done in moving a charge $q$ from $(a,\,0,\,0)$ to $(2a,\,0,\,0)$ is:

• A. $\dfrac{q\lambda}{2\pi\varepsilon_0}\ln 2$
• B. $\dfrac{q\lambda}{4\pi\varepsilon_0}\ln 2$
• C. $\dfrac{q\lambda}{2\pi\varepsilon_0}\ln\!\left(\tfrac{1}{2}\right)$
• D. zero

Hint:

The potential of an infinite line charge varies as $\ln r$ (not $1/r$), because its field falls off as $1/r$. So work done depends only on the ratio of distances, not their absolute values.

Answer 1

The Correct Option is A