Two large metal sheets carry surface currents as shown in figure. The current through a strip of width $dl$ is $Kdl$, where $K$ is a constant. Find the magnetic field at the point $P, Q$ and $R$.

 

Magnetic effect of the current and magnetic force on charge or current a neutron, a proton, an electron and an $\mathrm{\alpha }$-particle enters a uniform magnetic field with equal velocities. The field is directed along the inward normal to the plane of the paper. Which of these tracks followed are by electron and $\mathrm{\alpha }$-particle.

Two long parallel wires carrying currents $2.5 \stackrel{\circ }{\mathrm{A}}$ and $\mathrm{I} \stackrel{\circ }{\mathrm{A}}$ in the same direction (directed into the plane of the paper) are held at $P$ and $Q$, respectively, such that they are perpendicular to the plane of paper. The points $P$ and $Q$ are located at a distance of $5 \mathrm{m}$ and $2 \mathrm{m}$, respectively, from a collinear point $R$.

(a) An electron moving with a velocity of $4\times {10}^5 \mathrm{m} {\mathrm{s}}^{-1}$ along the positive $X$-direction experiences a force of magnitude $3.2\times {10}^{-20} \mathrm{N}$ at the point $R$. Find the value of $I$.

(b) Find all the positions at which a third long-parallel wire carrying a current of magnitude $2.5 \mathrm{A}$ may be placed so that the magnetic induction at $R$ is zero.

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.