An electron is rotating around an infinite po | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The centripetal force required for the circular motion of the electron is provided by the electrostatic force exerted by the infinite linear charg

Vedclass · Accepted Answer

$5.62$

Vedclass · Answer

(B) The centripetal force required for the circular motion of the electron is provided by the electrostatic force exerted by the infinite linear charge.The electric field $E$ at a distance $r$ from an infinite linear charge with density $\lambda$ is given by $E = \frac{\lambda}{2 \pi \varepsilon_0 r}$.The electrostatic force on the electron is $F = eE = e \cdot \frac{\lambda}{2 \pi \varepsilon_0 r}$.Equating this to the centripetal force $\frac{mv^2}{r}$,we get:$\frac{mv^2}{r} = \frac{e \lambda}{2 \pi \varepsilon_0 r}$Solving for $v$:$v = \sqrt{\frac{e \lambda}{2 \pi \varepsilon_0 m}} = \sqrt{\frac{2 k \lambda e}{m}}$,where $k = \frac{1}{4 \pi \varepsilon_0} = 9 	imes 10^9 \, N \cdot m^2/C^2$.Substituting the values: $e = 1.6 	imes 10^{-19} \, C$,$\lambda = 1 	imes 10^{-6} \, C/m$,$m = 9.1 	imes 10^{-31} \, kg$:$v = \sqrt{\frac{2 	imes 9 	imes 10^9 	imes 10^{-6} 	imes 1.6 	imes 10^{-19}}{9.1 	imes 10^{-31}}}$$v = \sqrt{\frac{28.8 	imes 10^{-16}}{9.1 	imes 10^{-31}}} = \sqrt{3.1648 	imes 10^{15}} \approx 5.62 	imes 10^7 \, m/s$.

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 the electron in $m/s$ will be ...... $\times 10^7$.

Similar Questions

$A$ particle of mass $0.5 \ g$ and charge $10 \ \mu C$ is subjected to a uniform electric field of $8 \ NC^{-1}$. If the particle is initially at rest,the velocity of the particle after a time of $5 \ s$ is: (in $ms^{-1}$)

An alpha particle and a proton are accelerated from rest in a uniform electric field. The ratio of the times taken by proton and alpha particle to attain equal displacements is

$A$ liquid drop having $6$ excess electrons is kept stationary under a uniform electric field of $25.5 \times 10^3 \, Vm^{-1}$. The density of the liquid is $1.26 \times 10^3 \, kg \, m^{-3}$. The radius of the drop is (neglect buoyancy):

$A$ water drop of mass $10^{-6} \ kg$ carries a charge of $(-10^{-6}) \ C$. What magnitude of electric field should be applied to the drop so that it is in equilibrium with its weight?

$A$ charged particle,initially at rest at $O$,follows the trajectory shown alongside when released. Such a trajectory is possible in the presence of:

Vedclass Test Series

Exam Paper Generator

Online Exam Module