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) :

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) : (A) (2eμ0 nIR/m) (B) (eμ0 nIR/2m) (C) (eμ0 nIR/4m) (D) (eμ0 nIR/m)

Tardigrade Admin · Accepted Answer

Top view of solenoid Maximum possible radius of electron = (R/2) ∴ (R/2) = (mv/qB) = (mvmax/e(μ0ni)) vmax = (R/2) (e μ 0ni/m)

$\frac{2 e μ _{0} n I R}{m}$

$\frac{e μ _{0} n I R}{2 m}$

$\frac{e μ _{0} n I R}{4 m}$

$\frac{e μ _{0} n I R}{m}$

Top view of solenoid
Maximum possible radius of electron $= \frac{R}{2}$
$∴ \frac{R}{2} = \frac{m v}{qB} = \frac{m v _{ma x}}{e ( μ _{0} ni )}$
$v_{ma x} = \frac{R}{2} \frac{e μ _{0} ni}{m}$

m2eμ0​nIR​

2meμ0​nIR​

4meμ0​nIR​

meμ0​nIR​

Top view of solenoid Maximum possible radius of electron =2R​ ∴2R​=qBmv​=e(μ0​ni)mvmax​​ vmax​=2R​meμ0​ni​

$\frac{2 e μ _{0} n I R}{m}$

$\frac{e μ _{0} n I R}{2 m}$

$\frac{e μ _{0} n I R}{4 m}$

$\frac{e μ _{0} n I R}{m}$

Top view of solenoid
Maximum possible radius of electron $= \frac{R}{2}$
$∴ \frac{R}{2} = \frac{m v}{qB} = \frac{m v _{ma x}}{e ( μ _{0} ni )}$
$v_{ma x} = \frac{R}{2} \frac{e μ _{0} ni}{m}$