Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismMotion analysis in electric & magnetic fieldEasy2 minPYQ_2020

PhysicsEasysingle choice

A proton, an electron and a Helium nucleus have the same kinetic energy. They are in circular orbits in a plane due to a magnetic field which is perpendicular to the plane. Let $r_{p}$ , $r_{e}$ and $r_{H e}$ be their respective radii, then

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Answer:

Solution:

Radius of circle is given by $r = \frac{m v}{q B} = \frac{p}{q B} = \frac{\sqrt{2 m K}}{q B} = \frac{\sqrt{2 m}}{q B} \sqrt{K}$ (where $K$ is kinetic energy)

For proton, $r_{p} = \frac{\sqrt{2 m_{p}}}{e B} \sqrt{K}$

For electron, $r_{e} = \frac{\sqrt{2 m_{e}}}{e B} \sqrt{K}$

For $H e^{2 +}, r_{H e} = \frac{\sqrt{2 \times 4 m_{p}}}{(2 e) B} \sqrt{K} = \frac{\sqrt{2 m_{p}}}{e B} \sqrt{K}$

Clearly, $r_{H e} = r_{p} > r_{e}$

Stream:JEESubject:PhysicsTopic:MagnetismSubtopic:Motion analysis in electric & magnetic field

⏱ 2mℹ️ Source: PYQ_2020

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