A charged particle of charge $q$ and mass $m$, gets deflected through an angle $\theta$ upon passing through a square region of side $a$, which contains a uniform magnetic field $B$ normal to its plane. Assuming that the particle entered the square at right angles to one side, what is the speed of the particle?
KVPY 2010, Diffcult
Download our app for free and get started
(a)
In given condition, if $r$ is radius of curved path travelled by changed particle.
Then,
$\sin \theta \approx \tan \theta=\frac{a}{r}$
or $\quad r=a \operatorname{cosec} \theta \approx a \cot \theta \quad \dots(i)$
Also, $\quad r=\frac{m v}{B q} \quad \dots(ii)$
Combining Eqs. $(i)$ and $(ii)$, we get
$v=\frac{q B}{m} a \cot \theta$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A moving coil galvanometer has a coil with $175\, turns$ and area $1\, cm^2$ It uses a torsion band of torsion constant $10^{-6}\, N\, -m/rad$. The coil is placed in a magnetic field $B$ parallel to its plane. The coil deflects by $10$ for a current of $1\, mA$. The value of $B$ (in Tesla) is approximatelyView Solution
- 2The dipole moment of a circular loop carrying a current $I$, is $m$ and the magnetic field at the centre of the loop is $B_1$ . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$ . The ratio $\frac{{{B_1}}}{{{B_2}}}$ isView Solution
- 3The magnetic field at the center of current carrying circular loop is $B _{1}$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_{2}$. The value of $B_{1} / B_{2}$ will be.View Solution
- 4A thin rod is bent in the shape of a small circle of radius $'r'$. If the charge per unit length of the rod is $'\sigma ',$ and if the circle is rotated about its axis at the rate of $'n'$ rotation per second, the magnetic induction at a point on the axis at a large distance $'y'$ from the centre isView Solution
- 5A long wire A carries a current of $10\, amp$. Another long wire $B$, Which is parallel to $A$ and separated by $0.1\,m$ from $A$, carries a current of $5\, amp$, in the opposite direction to that in $A$. what is the magnitude and nature of the force experienced per unit length of $B$ $({\mu _0} = 4\pi \times {10^{ - 7}}\,weber/amp{\rm{ - }}m)$View Solution
- 6Current $'i'$ is flowing in the rectangular loop placed in the $xyz$ plane as shown in the figure. Find the magnetic moment of the loopView Solution
- 7In toroid magnetic field on axis will be the radius $=0.5\, cm ,$ current $=1.5\, A ,$ turns $=250,$ permeability $=700$ (in Tesla)View Solution
- 8A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If $r_{d}$ and $r_{p}$ are the radii of their circular paths respectively, then the ratio $\frac{r_{d}}{r_{p}}$ will be $\sqrt{ x }: 1$ where $x$ is ..........View Solution
- 9A thin ring of $10\, cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\,\pi \,rad\,{s^{ - 1}}$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8 \times {10^{ - 9}}\,T$, then the charge carried by the ring is close to $\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,N/{A^2}} \right)$View Solution
- 10View SolutionMagnetic dipole moment of a rectangular loop is