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JEE Main 2019 (10 Apr, Shift 1) · Moving Charge in a Magnetic Field

Moving Charge in a Magnetic Field question from JEE Main 2019 (10 Apr, Shift 1)

Q87JEE Main 2019 · 10 APR · SHIFT 1Medium

Moving Charge in a Magnetic Field

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicualr to the plane. Let rp, re and rHe be their respective radii, then

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Answer: (b)

Equal energy: $r = \dfrac{\sqrt{2mK}}{qB} \Rightarrow r \propto \dfrac{\sqrt{m}}{q}$ .
Electron: $\dfrac{\sqrt{m_e}}{e}$ (smallest, since $m_e \ll m_p$ ); proton: $\dfrac{\sqrt{m_p}}{e}$ ; He: $\dfrac{\sqrt{4m_p}}{2e} = \dfrac{\sqrt{m_p}}{e}$ .
So $r_e < r_p = r_{He}$ .
So the answer is (b).

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