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  4. A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an deutron to describe a circle of same radius in the same field?

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Q. A proton carrying $1\, MeV$ kinetic energy is moving in a circular path of radius $R$ in uniform magnetic field. What should be the energy of an deutron to describe a circle of same radius in the same field?

Moving Charges and Magnetism

Solution:

$R =\frac{ mu }{ qB }$
$\Rightarrow KE =\frac{ q ^{2} B ^{2} R ^{2}}{2 m } \propto \frac{ q ^{2}}{ m }$
Since charge on both is same but mass of deutron is double of proton.
$( KE )_{\text {deutron }}=\frac{( KE )_{\text {proton }}}{2}=0.5 \,MeV$