Question

A tightly wound long solenoid has '$n$' turns per unit length, a radius ' $r$ ' and carries a current $I$. A particle having charge ' $q$ ' and mass '$m$' is projected from a point on the axis in a direction perpendicular to the axis. The maximum speed of the particle for which the particle does not strike the solenoid is

• A. $\frac{\mu_{0} nIqr }{ m }$
• B. $\frac{\mu_{0} nIqr }{2 m }$
• C. $\frac{\mu_{0} nIqr }{4 m }$
• D. $\frac{\mu_{0} nIqr }{8 m }$

Answer 1

Answer: (B)

$\frac{\mu_{0} nIqr }{2 m }$

Answer 2

$F _{ B } = qvB \sin \theta \,\, \theta = 90^{\circ}$ $F _{ B } = qvB$ $F _{ C } =\frac{ mv ^{2}}{ r }$ $F _{ B } = F _{ C }$ $qvB =\frac{ mv ^{2}}{\left(\frac{ r }{2}\right)}$ $v =\frac{ qrB }{2 m }$ $B =\mu_{0} nI$ $v =\frac{ qr \mu_{0} nI }{2 m }$