An electron gun is placed inside a long solenoid of radius R on its… | JEE Main 2020 (9 Jan, Shift 2)

Q82JEE Main 2020 · 9 JAN · SHIFT 2Difficult

Moving Charge in a Magnetic Field

An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current I. The electron gun shoots an electron along the radius of the solenoid with speed v. If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning):

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Answer: (c)

Inside the solenoid $B = \mu_0 nI$ along the axis; the electron, shot radially, moves in a circle of radius $r = \dfrac{mv}{eB}$ that passes through the axis.
Its farthest distance from the axis is the diameter $2r$ . To avoid the wall: $2r \le R$ .
$\dfrac{2mv}{e\mu_0 nI} \le R \Rightarrow v_{max} = \dfrac{e\mu_0 nIR}{2m}$
So the answer is (c).

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