Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field $B = B_0 \hat k$ .
Medium
Download our app for free and get started
For given pitch, $d$ corresponds to charged particle, we have
$\frac{\mathrm{q}}{\mathrm{m}}=\frac{2 \pi \mathrm{v} \cos \theta}{\mathrm{B}}=\mathrm{constant} \Rightarrow\left(\frac{\mathrm{e}}{\mathrm{m}}\right)_{1}+\left(\frac{\mathrm{e}}{\mathrm{m}}\right)_{2}=0$
Note Consider $e$ in place of $\mathrm{q}$ in solution.
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 thin flexible wire of length $\mathrm{L}$ is connected to two adjacent fixed points and carries a current $\mathrm{I}$ in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength $B$ going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire isView Solution
- 2Two long thin, parallel conductors carrying equal currents in the same direction are fixed parallel to the $x$-axis, one passing through $y = a$ and the other through $y = -a$. The resultant magnetic field due to the two conductors at any point is $B$. Which of the following are correct?View Solution
- 3Current $I$ is flowing in conductor shaped as shown in the figure. The radius of the curved part is $r$ and the length of straight portion is very large. The value of the magnetic field at the centre $O$ will beView Solution
- 4View SolutionA charged particle is released from rest in a region of uniform electric and magnetic fields which are parallel to each other. The particle will move on a
- 5Two concentric circular loops, one of radius $R$ and the other of radius $2 R$, lie in the $x y$-plane with the origin as their common center, as shown in the figure. The smaller loop carries current $I_1$ in the anti-clockwise direction and the larger loop carries current $I_2$ in the clockwise direction, with $I_2>2 I_1 . \vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $x y$-plane. Which of the following statement($s$) is(are) current?View Solution
$(A)$ $\vec{B}(x, y)$ is perpendicular to the $x y$-plane at any point in the plane
$(B)$ $|\vec{B}(x, y)|$ depends on $x$ and $y$ only through the radial distance $r=\sqrt{x^2+y^2}$
$(C)$ $|\vec{B}(x, y)|$ is non-zero at all points for $r$
$(D)$ $\vec{B}(x, y)$ points normally outward from the $x y$-plane for all the points between the two loops
- 6The maximum velocity to which a proton can be accelerated in a cyclotron of $10\, MHz$ frequency and radius $50\, cm$ isView Solution
- 7A circular coil of $1000\,turns$ and area of cross-section $1.5 \times 10^{-4}\, m^2$, is carrying a current of $2\,A$. What is the magnetic moment associated with the coil?....$Am^2$View Solution
- 8A galvanometer is used in laboratory for the null point in electrical experiments. If, on passing a current of $6 \,m A$ it produces a deflection of $2^{\circ},$ its figure of merit is close to :View Solution
- 9A milli voltmeter of $25\,millivolt$ range is to be converted in to an ammeter of $25\,A$ range. The value (in $ohm$) of necessary shunt will beView Solution
- 10A solenoid of $N$ turn, $'l'$ length and $'r'$ radius of cross - section. If current $i$ flow in solenoid then magnetic field at axial mid point will be (where $l\, \simeq \,\,r$ )View Solution