First slide

Force on a charged particle moving in a magnetic field

Question

In a nuclear experiment a 1 Mev proton moves in a uniform magnetic field in a circular path of a certain radius.The energy of a deuteron which will circulate in the same orbit in the same magnetic field will be

Moderate

A

1 Mev
B

4 Mev
C

0.5 Mev
D

2 Mev

Solution

$\begin{array}{l} ω = \frac{QB}{m}, Speed v = \sqrt{\frac{2 k}{m}} \\ ∴ K = \frac{1}{2} {mω}^{2} R^{2} = \frac{Q^{2} B^{2} R^{2}}{2 m} \\ ∴ \frac{k_{d}}{k_{p}} = (\frac{{Q_{d}}^{2}}{{Q_{p}}^{2}}) \times (\frac{m_{p}}{m_{d}}) = {(1)}^{2} \times \frac{1}{2} = \frac{1}{2} \\ ∴ k_{d} = 0 .5 Mev \end{array}$

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