Academic Experts Solutions for Chapter: Moving Charges and Magnetism, Exercise 3: Motion of a Charged Particle in Electric and Magnetic Field

An electron (mass$=9.1\times {10}^{-31} \mathrm{kg}$, charge $=-1.6\times {10}^{-19} \mathrm{C}$) experiences no deflection if subjected to an electric field of $3.2\times {10}^5 \mathrm{V} {\mathrm{m}}^{-1}$ and a magnetic field of $2.0\times {10}^{-3} \mathrm{Wb} {\mathrm{m}}^{-2}$. Both the fields are normal to the path of electron and to each other. If the electric field is removed, then the electron will revolve in an orbit of radius

An electron moving with a velocity $\overrightarrow{{\mathrm{v}}_1}=2\hat{\mathrm{i}} \mathrm{m} {\mathrm{s}}^{-1}$  at a point in a magnetic field experiences a force $\overrightarrow{{\mathrm{F}}_1}=-2\hat{\mathrm{j}} \mathrm{N}.$ If the electron is moving with a velocity $\overrightarrow{{\mathrm{v}}_2}=2\hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1}$ at the same point, it experiences a force $\overrightarrow{{\mathrm{F}}_2}=2\hat{\mathrm{i}} \mathrm{N}$. The force electron would experience if it were moving with a velocity $\overrightarrow{{\mathrm{v}}_3}=2\hat{\mathrm{k}} \mathrm{m} {\mathrm{s}}^{-1}$  at the same point is  

A particle of charge $q$ and mass $m$ starts moving from the origin in presence of an electric field $\overrightarrow{E}=E_0\hat{i}$ and a magnetic field $\overrightarrow{B}=B_0\hat{i}$ with a velocity $\overrightarrow{v}=v_0\hat{j}$. The speed of the particle will become $2v_0$ after a time $t$. Determine $t$.

A particle moving with a velocity $v$ having specific charge $\left(\frac{q}{m}\right)$ enters in a region of magnetic field $B$ having width $d=\frac{3mv}{5qB}$ at an angle ${53}^{\circ }$ to the boundary of magnetic field. Find the angle of emergence $\theta$.

A particle of mass $m$ and charge $q$, moves with a constant velocity $v$, along the positive $x$-direction. It enters a region containing a uniform magnetic field $B$, directed along the negative $z$-direction, extending from $x=a$ to $x=b.$ The minimum value of $v$ required, so that the particle can just enter the region $x>b$, is

A particle of mass $1.6\times {10}^{-27} \mathrm{kg}$ and charge $1.6\times {10}^{-19} \mathrm{C}$ enters in an uniform magnetic field of $1 \mathrm{T}$ as shown in the figure. The speed of the particle is ${10}^7 \mathrm{m} {\mathrm{s}}^{-1}$. The distance $\mathrm{PQ}$ will be

Two particles $A$ and $B$ of masses $m_A$ and $m_B$ respectively, having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are $v_A$ and $v_B$ respectively and the trajectories are as shown in the figure. Then

A particle of charge $+q$ and mass $m$, moving under the influence of a uniform electric field $E\hat{\mathrm{i}}$ and a uniform magnetic field $B\hat{\mathrm{k}}$, follows trajectory from $P$ to $Q$, as shown in the figure. The velocities at $P$ and $Q$ are $v\hat{\mathrm{i}}$ and $-2v\hat{\mathrm{j}}$, respectively. Which of the following options are correct?

(a) $E=\frac{3}{4}\frac{m{v}^2}{qa}$

(b)  $E= \frac{3}{2}\frac{m{v}^2}{qa}$

(c) Rate of work done by magnetic field at any point is zero.

(d) Rate of work done by electric field at any point is zero.