Question

An extremely long wire is uniformly charged. An electron is revolving around the wire and making ${10}^8$ revolutions per second in an orbit of radius $2cm$. Linear charge density of the wire is nearly ?

• A. $50nC/m$
• B. $25nC/m$
• C. $40nC/m$
• D. $12.5nC/m$

Answer 1

Answer: (A)

$50nC/m$

Given,

$\omega =2\pi \times {10}^{8}rad/s$

$r=2\times {10}^{-2}m$

We know,

Electric field=$E=\frac{2k\lambda }{r}$

$F=qE=m{\omega }^{2}r$

$\frac{2ke\lambda }{r}=m{\omega }^{2}r$

$\lambda =\frac{m{\omega }^2{r}^2}{2ke}$

$\lambda =\frac{9.1\times {10}^{-31}\times 4{\pi }^2\times {10}^{16}\times 4\times {10}^{-4}}{2\times 9\times {10}^9\times 1.6\times {10}^{-19}}$

$\lambda =50nC/m$

Option $\text{A}$ is the correct answer