​3.   If the first minima in a Young's slit experiment occurs directly in front of one of the slits, (distance between the slits & screen D = 12 cm and distance between slits D = 5 cm) then the wavelength of the radiation used can be :
(1) 2 cm         (2) 4 cm         (3) 1 cm         (4)  4 3
4.  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 of the solenoid in a direction perpendicular to the axis. What can be the minimum speed for which the particle should be projected to strike the solenoid?

(1)  μ 0niqr/m        (2)   μ 0niqr/2m        ​(3)  μ 0niqr/4m        ​(4) None

Dear student
ans 4.

Given:

Magnitude of current in the solenoid = i
Number of turns per unit length = n
When a particle is projected perpendicular to the magnetic field, it describes a circular path.
And for the particle (projected from a point on the axis in a direction perpendicular to the axis) to not strike the solenoid, the maximum radius of that circular path should be r/2.

∴ Radius of the circle = r2

We know,
Centripetal force = Magnetic force
mV2r=qVBV=qBrm=qμ0nir2m

Please post another query is separate thread.
Regards

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