Question

An infinitely long rod of negligible radius has a uniform charge density $\lambda =5mC/m$. Calculate the electric field at a distance $10m$ from the wire.

• A. $9\times {10}^{3}N/C$
• B. $9\times {10}^{-6}N/C$
• C. $9\times {10}^{6}N/C$
• D. $9\times {10}^{-3}N/C$

Answer 1

The correct option is C $9\times {10}^{6}N/C$

Field due to an infinite linear distribution of charge is given by-

$E=\frac{\lambda }{2\pi {ϵ}_{o}r}$

and $k=\frac{1}{4\pi {ϵ}_o}=9\times {10}^9$

$⟹\frac{1}{2\pi {ϵ}_o}=18\times {10}^9$

Now, $E=\frac{18\times {10}^9\times 5\times {10}^{-3}}{10}$

$⟹E=9\times {10}^{6}N/C$

Answer-(C)