Magnetic Effects & Magnetism

JEE Main level, single correct, medium

155 of 276

Question 155 of 276

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

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Answer: (A) eμ0nIRm\dfrac{e{\mu }_{0}nIR}{m}

Magnetic Field Inside Solenoid is B=μ0nIB={\mu }_{0}nI
Velocity ν\nu has given to the electron
So, Magnetic Force
F=qνBF=q\nu B
as ν\nuand BB are perpendicular.
In a magnetic field, charge will move on a circular path. Here, If radius is just less than or equal to radius of solenoid then the electron does not hit the surface.
F=qνB=mν2R⇒mν=qBRasq=eν=eBRmSo,V=eμ0nIRmF=q\nu B=\dfrac{m{\nu }^{2}}{R} \Rightarrow m\nu =qBR asq=e \nu =\dfrac{eBR}{m} So,V=\dfrac{e{\mu }_{0}nIR}{m}

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