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…

Question

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)

Accepted Answer

(4) (eμ₀ nIR)/(2m). Field inside: B = μ₀ nI along the axis; the electron moves on a circle of radius r = (mv)/(eB) in the cross-section. The circle passes through the axis, so its farthest point is 2r from the axis. No hit: 2r ≤ R, so r ≤ R/2. vₘₐₓ = (eBR)/(2m) = (eμ₀ nIR)/(2m).

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