Question

An electron is rotating around an infinite positive linear charge in a circle of radius 0.1 m, if the linear charge density is $1\mu C/m,$ then the velocity of electron in m/s will be

• A. $0.562\times {10}^7$
• B. $5.62\times {10}^7$
• C. $562\times {10}^7$
• D. $0.0562\times {10}^7$

Answer 1

The correct option is B $5.62\times {10}^7$

REF.Image.

solution

Consider a Gaussian surface

which is cylindrical

symmetrical about the damage

so, Net flux $=\frac{ginclosed}{{ϵ}_0}$

$\Rightarrow E\left(2\pi rl\right)=\frac{\lambda l}{e_0}$

$\Rightarrow E=\frac{\lambda }{2\pi r{ϵ}_0}$

Here, Electrostatic force = centripetal force

$\Rightarrow \left({\frac{\lambda }{2\pi rϵ}}_0\right)e=\frac{m{v}^2}{r}$

$\Rightarrow v=\sqrt{\frac{{\lambda }_0}{2\pi {ϵ}_0\pi }}=\sqrt{2\times \frac{9}{2}\times {10}^9\times {10}^{-6+3}\times 1.759\times {10}^8}$

$v=5.62\times {10}^7$ option - B is correct.