Discussion Forum

Two particles  X and Y have equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe circular paths of radii  r₁ and r₂ respectively. The ratio of the mass of X to that of Y is

Answer:

Explanation:

 According to question, force acting on the particle inside the magnetic field is given by

$F_{B}=qvB\sin \theta$

 [where  $\theta$= angle between  v and B]

 This force F_B provides necessary centripetal force for circular motion of the charged particle.

 So,  $\frac{mv^{2}}{r}=qvB\sin \theta$

 Now, for particles x and y and $\theta$ = 90°

 $\frac{m_{x}v_{x}^{2}}{r_{1}}=qv_{x}B$...................(i)

$\frac{m_{y}v_{y}^{2}}{r_{2}}=qv_{y}B$...........(ii)

 From Eqs.(i) and (ii) , we get

 $\frac{m_{x}v_{x}^{}}{m_{y}v_{y}^{}}=\frac{r_{1}}{r_{2}}$

 as, $\frac{v_{x}^{}}{v_{y}^{}}=1$

 So,   $\frac{m_{x}^{}}{m_{y}^{}}=\frac{r_{1}}{r_{2}}$