Question

An infinite line charge produces a field of 18*10(to the power of 10) N/C at a distance of 1m. The linear charge density is?

Answer 1

Step 1: Given

Field produced by line charge, $E=18\times {10}^{10}\frac{N}{C}$

Distance, $r=1m$

Let linear charge density be $\lambda$

Step 2: Calculation of linear charge density

Electric field due to linear charge density is given by,

$E=\frac{\lambda }{2\pi {\epsilon }_{o}r}$

$\Rightarrow 18\times {10}^{10}=\frac{2\lambda }{4\pi {\epsilon }_{o}r}$

$\Rightarrow 18\times {10}^{10}=\frac{2K\lambda }{r}$

$\Rightarrow 18\times {10}^{10}=\frac{2\times 9\times {10}^9\lambda }{1}$

$\Rightarrow \lambda =10\frac{C}{m}$

Hence, linear charge density is $10C/m$.