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Magnetism

Section: Physics

Question : 46 of 46

Marks: +1, -0

The particle enters Region III only if its velocity is V > $\frac{qlB}{m}$ .
The particle enters Region III only if its velocity V < $\frac{qlB}{m}\text{. }$
Path length of the particle in Region II is maximum when velocity V = $\frac{qlB}{m}$ .
Time spent in Region II is same for any velocity V as long as the particle returns to Region I.

Solution:

The particle enters the Region III only when the cyclotron radius r is greater than l, that is, r > l.

v >

\frac{qBl}{m}

⇒

\frac{mv}{qB}

> l

The path length is maximum when the radius of curvature r = l.

If r < l, particle traces a semi-circle inside

\overset{\rightarrow}{B}

. The time taken t =

\frac{T}{2}

\frac{\pi m}{qB}

is independent of velocity, v. So the time spent in Region II is independent of velocity.

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