Question

Electric field produced due to an infinitely long straight uniformly charged wire at perpendicular distance of $2cm$ is $3\times {10}^{8}N{C}^{-1}$. Then, linear charge density on the wire is _____________.
$(K=9\times {10}^{9}SIunit)$

• A. $3.33\frac{\mu C}{m}$
• B. $333\frac{\mu C}{m}$
• C. $666\frac{\mu C}{m}$
• D. $6.66\frac{\mu C}{m}$

Answer 1

The correct option is B $333\frac{\mu C}{m}$

Given, $r=2\times {10}^{-2}m$,
$E=3\times {10}^{8}N/C$
$K=9\times {10}^{9}N{m}^2/C^2$
The linear charge density $I=\frac{E\cdot r}{2K}$
$\Rightarrow I=\frac{3\times {10}^8\times 2\times {10}^{-2}}{2\times 9\times {10}^9}$
$\Rightarrow I=\frac{1}{3}\times {10}^{-3}C/m$
$\Rightarrow =0.333\times {10}^{-3}C/m$
$=333\times {10}^{-6}C/m$
$=333\mu C/m$