A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to $4$ times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle
A$1: 1$
B$1: 2$
C$2: 1$
D$1: 4$
JEE MAIN 2022, Medium
Download our app for free and get started
C$2: 1$
c radius of paerticle in cyclotron
$r =\frac{\sqrt{2 mK . E .}}{ qB }$
So ratio of new radius to original
$\frac{ r _{ n }}{ r _{0}}=\sqrt{\frac{( K \cdot E .)_{ n }}{( K \cdot E )_{0}}}=\sqrt{4} \Rightarrow 2: 1$
Download our app
and 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.*
The ratio of the magnetic field at the cpentre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be
A proton and a deutron ( $\mathrm{q}=+\mathrm{e}, m=2.0 \mathrm{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is:
Ionized hydrogen atoms and $\alpha$ -particles with same momenta enters perpendicular to a constant magnetic field $B$. The ratio of their radii of their paths $\mathrm{r}_{\mathrm{H}}: \mathrm{r}_{\alpha}$ will be
The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of $10\, g$ and is $5\, cm$ long. The wire is hanging as shown in the figure. The springs stretch $0.5\, cm$ under the weight of the wire and the circuit has a total resistance of $12\, \Omega $. When the lower wire is subjected to a static magnetic field, the springs, stretch an additional $0.3\, cm$. The magnetic field is
Two ions having same mass have charges in the ratio $1: 2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2: 3$. The ratio of the radii of their circular trajectories is -
Two mutually perpendicular conductors carrying currents $I_1$ and $I_2$ lie in one plane. Locus of the point at which the magnetic induction is zero, is a