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Question

A proton and an alpha particle enter into a uniform magnetic field with the same velocity.The period of rotation of the alpha particle will be


A
four times that of proton
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B
two times that of proton
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C
three times that of proton
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D
same as that of proton
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Solution

The correct option is C two times that of proton
$$T = \dfrac{2\pi m}{qB}$$
So, $$T \alpha \dfrac{m}{q}$$     (Taking B as same)
So, $$\alpha -particle$$ has 4 times mass of proton and 2 times charge of proton.
So, $$T\alpha = \dfrac{4m}{2q}$$    (taking mass of proton = m, Charge of proton = q)
So, $$T\alpha = 2 Tp$$

Physics

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