Magnetic Effects Of Current Question 259
Question: A proton (mass m and charge +e) and an $ \alpha - $ particle (mass 4m and charge +2e) are projected with the same kinetic energy at right angles to the uniform magnetic field. Which one of the following statements will be true [NCERT 1983]
Options:
A) The $ \alpha - $ particle will be bent in a circular path with a small radius that for the proton
B) The radius of the path of the $ \alpha - $ particle will be greater than that of the proton
C) The $ \alpha - $ particle and the proton will be bent in a circular path with the same radius
D) The $ \alpha - $ particle and the proton will go through the field in a straight line
Show Answer
Answer:
Correct Answer: C
Solution:
$ r=\frac{\sqrt{2mK}}{qB}i.e.\ r\propto \frac{\sqrt{m}}{q} $ Here kinetic energy K and B are same.
$ \therefore \frac{r_{p}}{{r_{\alpha }}}=\frac{\sqrt{m_{p}}}{\sqrt{{m_{\alpha }}}}.\frac{{q_{\alpha }}}{q_{p}}=\frac{\sqrt{m_{p}}}{\sqrt{4m_{p}}}.\frac{2q_{p}}{q_{p}}=1 $
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