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When a charged particle moving with velocity v enters a region containing a perpendicular magnetic field, it moves along a semi-circular path of radius r as shown in the figure.

Consider the following two statements.
I. The radius r of the semicircle is proportional to the initial speed v.
II. The time required for the particle to traverse the semicircle is independent of v.
Then

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Both I and II are true

Both I and II are incorrect

I is incorrect while II is true

I is true , but II is incorrect

answer is C.

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Detailed Solution

$\frac{{mv}^{2}}{r} = qvB \Rightarrow r = \frac{mv}{qB}$

and $t = \frac{2 π r}{v} = \frac{2 π m}{q B}$

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