Question

Two like charged infinitely long parallel wires with the same linear charge density of $3\times {10}^{8}C/cm$ are 2 cm apart. The work done against electrostatic force per unit length to be done in bringing them closer by 1 cm is $\frac{x}{100}J/m$. Find the value of x.

Answer 1

The electric field at distance x from an infinite line of charge (linear charge density, $\lambda$) is
$E=\frac{1}{4\pi {ϵ}_0}\frac{2\lambda }{x}$
So, force per unit length is,
$F=qE$

$F=\frac{{\lambda }_1{\lambda }_{2}l}{2\pi {ϵ}_{o}r}$

$F^{\prime }=\frac{F}{l}$

$using{\lambda }_1={\lambda }_2$

$F^{\prime }=8N$

Therefore, the work done is,

$W=F^{\prime }s$
$\Rightarrow W=8\times 1cm$
$\Rightarrow W=\frac{8}{100}J/C$
$\therefore x=8$