question_answer

Magnetic inductance B exists as shown in the figure. On the other side of line, a charged particle of charge q, mass m enters the magnetic field at\[{{45}^{o}}\]. The displacement of the particle when it emerges out of the magnetic field will be (velocity of the particles is V)                        

A)  \[\frac{\sqrt{2}m\,\,V}{qB}\]                

B)  \[\left( \frac{mV}{qe} \right)\]

C)  \[\frac{m\upsilon }{\sqrt{2q\,B}}\]                        

D)  \[\frac{\sqrt{3m\,V}}{qB}\]

Correct Answer: A

Solution :

From the figure. Displacement   \[S=2AC\,\,\cos \,\angle ACB\]                 \[=2\frac{mV}{qB}\times \frac{1}{2}=\sqrt{2}\frac{mV}{qB}\]