Embibe Experts Solutions for Exercise 5: EXERCISE

Find instantaneous direction of force in following cases (magnetic field, velocity are indicated)

Two protons enter a region of transverse magnetic field. What will be ratio of time period of revolution if the ratio of energy is $2\sqrt{2}:\sqrt{3} ?$

A charge $q,$ mass $m,$ travelling with speed $v$ enters a region of magnetic field at an angle $\theta$ with magnetic field. Mark the following statements as true or false.

$\left(\mathrm{a}\right)$ Kinetic energy of particle remains constant irrespective of $\theta$

$\left(\mathrm{b}\right)$ Velocity of particle remains constant if $\theta =n\pi ,$ where $n$ is an integer

$\left(\mathrm{c}\right)$ Speed of particle remains constant

$\left(\mathrm{d}\right)$ Acceleration of particle remains constant if $\theta =\left(2n-1\right)\frac{\pi }{2}$

$\left(\mathrm{e}\right)$ Average velocity of particle becomes negligible if $\theta =\left(2n-1\right)\frac{\pi }{2}$ over a long time

A charge $q$ and mass $m$ moving with velocity $v$ enters a region of magnetic field $B$ at an angle $\theta .$ Which of the following represents the correct graph for pitch w.r.t. angle $\theta ?$

A particle of charge $q,$ mass $m,$ moving with velocity $v_0(\hat{i}+\hat{j})$ enters a region of uniform magnetic field $B_0\hat{i}.$ Find displacement of particle after time $t=\frac{\pi m}{qB}.$

A particle of charge $q,$ mass $m,$ moving with velocity $v_0\left(\hat{i}+\hat{j}\right)$enters a region of uniform magnetic field $B_0\hat{i}.$ Find displacement of particle after time $t=\frac{2\pi m}{qB}.$

A particle of charge $q,$ mass $m,$ moving with velocity $v_0(\hat{i}+\hat{j})$ enters a region of uniform magnetic field $B_0\hat{i}$ Find displacement of particle for any arbitrary time $t.$