An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, r α respectively in a uniform magnetic field B. The relation between re, rp, r α is: (a) re rp = r α (c) re < rp = r α (d) re < rp < r α

Answer: (c). Equal K: r ∝ √(m)/q. Electron: (√(me))/(e) (smallest); proton: (√(mp))/(e); alpha: (√(4mp))/(2e) = (√(mp))/(e). So re < rp = rα. So the answer is (c).

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Moving Charge in a Magnetic Field

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, r $\alpha$ respectively in a uniform magnetic field B. The relation between re, rp, r $\alpha$ is:

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Answer: (c)

Equal $K$ : $r \propto \dfrac{\sqrt{m}}{q}$ .
Electron: $\dfrac{\sqrt{m_e}}{e}$ (smallest); proton: $\dfrac{\sqrt{m_p}}{e}$ ; alpha: $\dfrac{\sqrt{4m_p}}{2e} = \dfrac{\sqrt{m_p}}{e}$ .
So $r_e < r_p = r_\alpha$ .
So the answer is (c).

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