An experimenter’s diary reads as follows, a charged particle is projected in a magnetic field of $\left(7.0\hat{\mathrm{i}}–3.0\hat{\mathrm{j}}\right)\times {10}^{–3} \mathrm{T}$. The acceleration of the particle is found to be $\left(x\hat{\mathrm{i}}+7.0\hat{\mathrm{j}}\right)\times {10}^{–6} \mathrm{m} {\mathrm{s}}^{-2}$. Find the value of $x$.

A particle of mass $m$ and positive charge $q$, moving with a uniform velocity $v$, enters a magnetic field $B$ as shown in the figure. $\left(\mathrm{a}\right)$ Find the radius of the circular arc it describes in the magnetic field. $\left(\mathrm{b}\right)$ Find the angle subtended by the arc at the centre. $\left(\mathrm{c}\right)$ How long does the particle stay inside the magnetic field? $\left(\mathrm{d}\right)$ Solve the three parts of the above problem if the charge $q$ on the particle is negative.

A particle of mass $m$ and charge $q$ is projected into a region having a perpendicular magnetic field $B$. Find the angle of deviation (figure) of the particle as it comes out of the magnetic field if the width $d$ of the region is very slightly smaller than

$\left(\mathrm{a}\right) \frac{mv}{qB}$ $\left(\mathrm{b}\right) \frac{mv}{\sqrt{2}qB}$ and $\left(\mathrm{c}\right) \frac{3mv}{qB}$

The figure shows a convex lens of focal length $10 \mathrm{cm}$ lying in a uniform magnetic field $B$ of magnitude $1.2 \mathrm{T}$ parallel to its principal axis. A particle having a charge $2.0\times {10}^{–3} \mathrm{C}$ and mass $2.0\times {10}^{–5} \mathrm{kg}$ is projected perpendicular to the plane of the diagram with a speed of $4.8 \mathrm{m} {\mathrm{s}}^{-1}$. The particle moves along a circle with its centre on the principal axis at a distance of $15 \mathrm{cm}$ from the lens. The axis of the lens and of the circle are the same. Show that the image of the particle goes along a circle and find the radius of that circle.

An electron gun $\mathrm{G}$ emits electron of energy $2 \mathrm{keV}$ travelling in the positive $x-$direction. The electrons are required to hit the spot $S$ where $\mathrm{GS}=0.1 \mathrm{m}$ and the line $\mathrm{GS}$ makes an angle of $60°$ with the $x-$axis, as shown in the figure. A uniform magnetic field $B$ parallel to $\mathrm{GS}$ exists in the region outside of electron gun. Find the minimum value of $\mathrm{B}$ needed to make the electron hit $\mathrm{S}$. [Take mass of electron $= 9 \times {10}^{–31} \mathrm{kg}$]