(B) The magnetic field inside a long solenoid is $B = \mu_{0} nI$. When an electron is projected radially with speed $v$,it experiences a Lorentz forc

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

(B) The magnetic field inside a long solenoid is $B = \mu_{0} nI$. When an electron is projected radially with speed $v$,it experiences a Lorentz force $F = evB$ perpendicular to its velocity,causing it to move in a circular path of radius $r = \frac{mv}{eB}$.For the electron not to hit the surface of the solenoid of radius $R$,the diameter of its circular path must be less than or equal to the radius of the solenoid. Thus,$2r \leq R$,which implies $r \leq \frac{R}{2}$.Substituting $r = \frac{mv}{e(\mu_{0} nI)}$,we get $\frac{mv}{e\mu_{0} nI} \leq \frac{R}{2}$.Therefore,the maximum speed $v_{\max}$ is $\frac{e \mu_{0} nIR}{2m}$.

Class 12 Physics Moving Charges and Magnetism Motion of Charged Particle In Magnetic Field

Medium

An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ turns per unit length and carries a current $I$. The electron gun shoots an electron along the radius of the solenoid with speed $v$. If the electron does not hit the surface of the solenoid,the maximum possible value of $v$ is (all symbols have their standard meaning):

JEE MAIN 2020 All JEE MAIN

A
$\frac{e \mu_{0} nIR}{m}$
B
$\frac{e \mu_{0} nIR}{2 m}$
C
$\frac{2 e \mu_{0} nIR}{m}$
D
$\frac{e \mu_{0} nIR}{4 m}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Moving Charges and Magnetism

Subtopic

Motion of Charged Particle In Magnetic Field

Previous Year

JEE MAIN 2020 Paper All JEE MAIN years →

In an experiment,electrons are accelerated from rest by applying a voltage of $500 \, V$. Calculate the radius of the path if a magnetic field of $100 \, mT$ is then applied. [Charge of the electron $= 1.6 \times 10^{-19} \, C$,Mass of the electron $= 9.1 \times 10^{-31} \, kg$]

MediumJEE MAIN 2019

View Solution

An electric charge moving with uniform velocity has

EasyMHT CET 2022

View Solution

$A$ particle of mass $m$ and charge $q$,moving with velocity $V$,enters region $II$ normal to the boundary as shown in the figure. Region $II$ has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the region $II$ is $l$. Choose the incorrect option.

View Solution

$A$ proton,a deuteron and an $\alpha$-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If ${r_p}$,${r_d}$ and ${r_\alpha}$ denote respectively the radii of the trajectories of these particles,then:

Difficult

View Solution

Two particles $A$ and $B$ have equal charges but different masses $M_{A}$ and $M_{B}$. After being accelerated through the same potential difference,they enter a region of uniform magnetic field and describe paths of radii $R_{A}$ and $R_{B}$ respectively. Then $M_{A} : M_{B}$ is

EasyMHT CET 2020

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

In an experiment,electrons are accelerated from rest by applying a voltage of $500 \, V$. Calculate the radius of the path if a magnetic field of $100 \, mT$ is then applied. [Charge of the electron $= 1.6 \times 10^{-19} \, C$,Mass of the electron $= 9.1 \times 10^{-31} \, kg$]

An electric charge moving with uniform velocity has

$A$ particle of mass $m$ and charge $q$,moving with velocity $V$,enters region $II$ normal to the boundary as shown in the figure. Region $II$ has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the region $II$ is $l$. Choose the incorrect option.

$A$ proton,a deuteron and an $\alpha$-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If ${r_p}$,${r_d}$ and ${r_\alpha}$ denote respectively the radii of the trajectories of these particles,then:

Two particles $A$ and $B$ have equal charges but different masses $M_{A}$ and $M_{B}$. After being accelerated through the same potential difference,they enter a region of uniform magnetic field and describe paths of radii $R_{A}$ and $R_{B}$ respectively. Then $M_{A} : M_{B}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module