Question

Two infinite linear charges are placed parallel at $0.1m$ apart. If each has charge density of $5\mu C/m$, then the force per unit length of one of linear charges in $N/m$ is

• A. $2.5$
• B. $3.25$
• C. $4.5$
• D. $7.5$

Answer 1

The correct option is C $4.5$

we have the electric field intensity

$\overline{E}=\frac{q}{u\pi t_0{r}^2}$

we also know the

$F=E.q$

we have the find force per unit length

$uF/l=\frac{Eq}{l}$

$=\frac{\frac{q}{u\pi t_0{r}^2}.q}{l}=\frac{q^2}{u\pi t_0{r}^2}$

$q=5\mu c/m$

$r=0.1$

$\frac{F}{l}=\frac{5\times {10}^{-6}\times 5\times {10}^{-6}}{2\times 3.14\times 8.857\times {10}^{-12}\times 8.1}$

$=\frac{25}{6.28\times 0.8857}=4.494$

$=4.5N/m$

$Answer\$4.5N/m$