SATHEE: Magnetics 1 Question 15

Magnetics 1 Question 15

15. A proton, a deutron and an $α$ -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r_{p}, r_{d}$ and $r_{α}$ denote, respectively the radii of the trajectories of these particles, then

(1997, 1M)

(a) $r_{α} = r_{p} < r_{d}$

(b) $r_{α} > r_{d} > r_{p}$

(d) $r_{p} = r_{d} = r_{α}$

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Answer:

Correct Answer: 15. (a)

Solution:

Radius of the circular path is given by

$r = \frac{m v}{B q} = \frac{\sqrt{2 K m}}{B q}$

Here, $K$ is the kinetic energy to the particle.

Therefore, $r \propto \frac{\sqrt{m}}{q}$ if $K$ and $B$ are same.

$∴ r_{p} : r_{d} : r_{α} = \frac{\sqrt{1}}{1} : \frac{\sqrt{2}}{1} : \frac{\sqrt{4}}{2} = 1 : \sqrt{2} : 1$

Hence,

$r_{α} = r_{p} < r_{d}$

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Magnetics 1 Question 15

15. A proton, a deutron and an α-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp,rd and rα denote, respectively the radii of the trajectories of these particles, then

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15. A proton, a deutron and an $α$ -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r_{p}, r_{d}$ and $r_{α}$ denote, respectively the radii of the trajectories of these particles, then