Question

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?

Answer 1

Explanation:

Step 1:

Given data in the question

Magnitude of solenoid current = I

Number of revolutions per unit length = n

Step 2:

When an object is directed perpendicular to the magnetic area, this defines a circular direction.

And that the particle doesn't hit the solenoid (Projected in a path perpendicular to the axis from the point of the polarity), This circular path should have an average radius = $\frac{r}{2}$

∴ circle of the Radius $=\frac{r}{2}$

Step 3:

We know that

Centripetal force is equal to  Magnetic force

$\frac{m V^{2}}{r}=q V B |$

$V=\frac{q B r}{m}$

$=\frac{q \mu_{0} n i}{2 m}$

Answer 2

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Above answer is correct