A tightly-wound, long solenoid has n turns per unit length, a radius r and carries a current i. A particle having charge q and mass m is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed for which the particle does not strike the solenoid ?

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Solution

Given, current in solenoid = i

Number of turns per unit length = n

Radius of circle = $\frac{r}{2}$

We know that $\frac{m V^{2}}{R} = q V B$

$\Rightarrow V = \frac{q B R}{m} = \frac{q μ_{0} n i r}{2 m}$

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