Question:
A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces action on them is______ and their speed is_______ in the ratio.
Correct Option: 1
Solution:
(1)
As $v=\frac{p}{m} \& F=q v B$
$\therefore F=\frac{q p}{m} B$
$F_{1}=\frac{q p B}{m}, v_{1}=\frac{p}{m}$
$F_{2}=\frac{q p B}{2 m}, v_{2}=\frac{p}{2 m}$
$F_{3}=\frac{2 q p B}{4 m}, v_{3}=\frac{p}{4 m}$
$F_{1}: F_{2}: F_{3} \& V_{1}: V_{2}: V_{3}$
$\begin{array}{ll}1: \frac{1}{2}: \frac{1}{2} & \& 1: \frac{1}{2}: \frac{1}{4} \\ 2: 1: 1 & \& 4: 2: 1\end{array}$