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Moving Charges and Magnetism

Motion in a Magnetic Field

Proton, deuteron and alpha particle of same kinetic energy are

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Solving time: 4 mins

Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_{p}, r_{d}$ and $r_{α}$ . Which one of the following relation is correct?

Name: Video solution 1: Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rp,rd and rα. Which one of the following relation is correct?
Uploaded: 2023-02-12T14:13:06.000Z
Duration: 9 min
Description: Video solution 1: Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rp,rd and rα. Which one of the following relation is correct?

r_{α} = r_{p} = r_{d}

r_{α} = r_{p} < r_{d}

r_{α} > r_{d} > r_{p}

r_{α} = r_{d} > r_{p}

Views: 5,380 students

Updated on: Feb 20, 2023

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James Discussed

Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively

r_{p}, r_{d}

and

r_{α}

. Which one of the following relation is correct?

10 mins ago

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10 mins ago

Text solutionVerified

\frac{m v ^{2}}{r} = q v B

\Rightarrow r = \frac{m v}{qB}

But,

KE = \frac{p ^{2}}{2 m} \Rightarrow p = 2 mKE

Here, KE and B are same for the three particles

∴ r \propto \frac{m}{q}

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

\Rightarrow r_{α} = r_{p} < r_{d}

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Question Text	Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_{p}, r_{d}$ and $r_{α}$ . Which one of the following relation is correct?
Updated On	Feb 20, 2023
Topic	Moving Charges and Magnetism
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	298
Avg. Video Duration	10 min

Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_{p}, r_{d}$ and $r_{α}$ . Which one of the following relation is correct?

Text solutionVerified

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Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rp​,rd​ and rα​. Which one of the following relation is correct?

Text solutionVerified

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Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_{p}, r_{d}$ and $r_{α}$ . Which one of the following relation is correct?