Question

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

• A. $\frac{{\mu }_{o}qrni}{2m}$
• B. $\frac{{\mu }_{o}qrni}{m}$
• C. $\frac{2{\mu }_{o}qrni}{3m}$
• D. None of these

Answer 1

The correct option is A $\frac{{\mu }_{o}qrni}{2m}$

$\frac{r}{2}$= radius of circular path

$=\frac{mv}{Bq}=\frac{mv}{\left({\mu }_{o}ni\right)\left(q\right)}$

$\therefore v=\frac{{\mu }_{o}qrni}{2m}$