A direct current i flowing through the winding of a long cylindrical solendoid of radius R produces in it a uniform magnetic field. An electron (mass m and charge q) flies into the solenoid along the radius between the turns (at right angles to the solenoid axis) at velocity v. After a certain time, the electron deflected by the magnetic field leaves the solenoid. Then the time during which the electron remains inside the solenoid is [n is number of turns per unit length]

Engineering

Physics

Magnetic Field

Solenoid and Toroid

Motion of Charged Particle in Uniform Magnetic Field

Question

A direct current i flowing through the winding of a long cylindrical solendoid of radius R produces in it a uniform magnetic field. An electron (mass m and charge q) flies into the solenoid along the radius between the turns (at right angles to the solenoid axis) at velocity v. After a certain time, the electron deflected by the magnetic field leaves the solenoid. Then the time during which the electron remains inside the solenoid is [n is number of turns per unit length]

$\frac{m}{μ_{0} niq} [π - \tan^{- 1} \frac{mv}{μ_{0} niRq}]$

$\frac{2 m}{μ_{0} niq} [π - \tan^{- 1} \frac{mv}{μ_{0} niRq}]$

None of these

$\frac{m}{μ_{0} niq} [π - 2 \tan^{- 1} \frac{mv}{μ_{0} niRq}]$

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$t = \frac{mθ}{qB}$

$t = \frac{m}{qB} [2 \tan^{- 1} \frac{R}{R_{0}}] = \frac{2 m}{qB} [\frac{π}{2} - \tan^{- 1} \frac{R_{0}}{R}]$

$t = \frac{2 m}{{qμ}_{0} ni} [\frac{π}{2} - \tan^{- 1} (\frac{mv}{{qμ}_{0} niR})]$

$or \frac{2 m}{{qμ}_{0} ni} {\tan^{- 1} (\frac{{qμ}_{0} niR}{mv})}$