Magnetic Effects Of Current Question 404
Question: Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $ R_{1} $ and $ R_{2} $ respectively. The ratio of the mass of X to that of Y is
Options:
A) $ {{(R_{1}/R_{2})}^{1/2}} $
B) $ R_{2}/R_{1} $
C) $ {{(R_{1}/R_{2})}^{2}} $
D) $ R_{1}/R_{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] K.E. of first particle $ =\frac{1}{2}m_{1}v_{1}^{2}=qV $ …. (i) K.E. of second particle $ =\frac{1}{2}m_{2}v_{2}^{2}=qV $ After entering the magnetic field, a magnetic force acts on the charged particle which moves the charged particle in circular path of radius $ R=\frac{\sqrt{2mK}}{qB} $ Here, K, q, B are equal
$ \therefore R^{2}\propto m\Rightarrow \frac{m_{1}}{m_{2}}=\frac{R_{1}^{2}}{R_{2}^{2}} $ From (i) and (ii)
BETA
