$X-Y$ plane shown in the figure contains uniform magnetic field $\overrightarrow{B}=Bk$ for $y>0$. A particle having charge $q$ and mass $m$ travels along $y$-axis. At origin of co-ordinate system velocity of particle is $V_0$ and it enters the region containing magnetic field. Assume that particle is subjected to a frictional force $\overrightarrow{f}=-\alpha \overrightarrow{v}$ i.e. frictional force is proportional to velocity. Assume frictional force is large enough so that particle remains inside region $y>0$ at all times. The only forces acting on particle are frictional force and magnetic force. Particle will remain in $x-y$ plane as no magnetic force will act along $z$ axis. So $\overrightarrow{F}=-\alpha \overrightarrow{v}+q\overrightarrow{v}\times \overrightarrow{B}$. The $x-$ cordinate where particle comes to rest is given by $\frac{\lambda qBmV}{{\alpha }^2+{\left(qB\right)}^2}$. Find $\lambda$.

 

Two magnetic dipoles $\mathrm{X}$ and $\mathrm{Y}$ are placed at a separation $\mathrm{d}$ , with their axes perpendicular to each other. The dipole moment of $\mathrm{Y}$ is twice that of $\mathrm{X}$ . A particle of charge $\mathrm{q}$ is passing through their mid-point $\mathrm{P}$ , at angle $\mathrm{\theta }={45}^{\mathrm{o}}$ with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? ( $\mathrm{d}$ is much larger than the dimension of the dipole)

Consider a negatively charged particle moving with a velocity $v$ in a magnetic field $B$ applied perpendicular to the plane of the paper (into the paper). The particle follows the path $A$ or $B$ or $C$ or $D$ (shown in the figure)

An electron enters a magnetic field of $\left(3 \hat{i}+4 \hat{j}\right) \mathrm{T}$ with a velocity of $\left(6 \hat{j}+4 \hat{k}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ The acceleration produced is

($\frac{e}{m}$ of electron $=1.76\times {10}^{11} \mathrm{C} {\mathrm{kg}}^{-1}$)

A particle with charge $q$ moves with a velocity $v$ in a direction perpendicular to the directions of uniform electric and magnetic fields, $E$ and $B$ respectively, which are mutually perpendicular to each other. Which one of the following gives the condition for which the particle moves undeflected in its original trajectory?

An electric current $I$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. A particle carrying a charge $q$ moves along the axis of the circular wire with speed $v$. What is the magnetic force experienced by the particle when it passes through the centre of the circle?