Question

The electric field $10cm$ from a long wire is $2.4kN/C$. If wire carries uniform charge, what will be the field strength at $40cm$ from the wire?

• A. $0.6kN/C$
• B. $150N/C$
• C. $75N/C$
• D. $4.8kN/C$

Answer 1

The correct option is A $0.6kN/C$

Electric field due to long wire $=\frac{\lambda }{2\pi {ϵ}_{0}r}.$
($r$ = perpendicular distance from wire)
$E\propto \frac{1}{r}$
$E_1\propto \frac{1}{r_1}$
$E_2\propto \frac{1}{r_2}\Rightarrow \frac{E_1}{E_2}=\frac{r_2}{r_1}=\frac{40}{10}=4$
$E_2=\frac{E_1}{4}=\frac{2.4}{4}=0.6kN/C$