JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Magnetic Effects of Current

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):

(A) $\frac{2 e μ _{0} n I R}{m}$
(B) $\frac{e μ _{0} n I R}{m}$
(C) $\frac{e μ _{0} n I R}{4 m}$
(D) $\frac{e μ _{0} n I R}{2 m}$ ✓ Correct

Answer: (D)

Solution

On the axis the solenoid's field is

B = μ_{0} n I

directed along the axis, so an electron fired radially with speed

v

curves in a circle of radius

r = \frac{m v}{e B}

in the plane perpendicular to the axis. Starting from the axis, the electron stays inside the solenoid only while the diameter of this circle does not exceed

R

, so the largest permissible circle has radius

r = \frac{R}{2}

. Setting

\frac{R}{2} = \frac{m v _{m a x}}{e μ _{0} n I}

and solving gives

v_{m a x} = \frac{e μ _{0} n I R}{2 m}

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Single correct option

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JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Magnetic Effects of Current

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