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  4. A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio

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Q. A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio

J & K CETJ & K CET 2010Moving Charges and Magnetism

Solution:

Radius of the path $r=\frac{\sqrt{2} m K}{q B}$ or $r \propto \frac{\sqrt{1}}{q}$
$r_{p}: r_{d}: r_{\alpha}=\frac{\sqrt{1}}{q_{p}}: \frac{\sqrt{1}}{q_{d}}: \frac{\sqrt{1}}{q_{\alpha}}$
$\frac{1}{1}: \frac{1}{1}: \frac{1}{2}=2: 2: 1$