question_answer

A particle with a specific charge s is fired with a speed\[\upsilon \]towards a wall at a distance d, perpendicular to the wall. What minimum magnetic field must exist in this region for the particle not to hit the wall?

A) \[\frac{\upsilon }{sd}\]                                   

B) \[\frac{2\upsilon }{sd}\]                     

C)      \[\frac{\upsilon }{2sd}\]                     

D)      \[\frac{\upsilon }{4sd}\]                     

Correct Answer: A

Solution :

Let the radius of trajectory of the particle be R For the particle not to hit the wall \[R\le d\Rightarrow \frac{mv}{qB}\le d\] \[\therefore \]    \[B\ge \frac{mv}{qd}=\frac{v}{sd}\Rightarrow {{B}_{\min }}=\frac{v}{sd}\] Hence, the correction option is (a).