2019 Moving Charges and MagnetismMotion in Combined Electric and Magnetic Fields Medium Question 3 of 13 in Motion in Combined Electric and Magnetic Fields

Ionized hydrogen atoms and $\alpha$-particles with same momenta enters perpendicular to a constant magnetic field, $B$. The ratio of their radii of their paths $r_H:r_\alpha$ will be:

A $2:1$
B $1:2$
C $4:1$
D $1:4$

The answer is A.

Solution

Radius of the path in a magnetic field: $r=\frac{p}{qB}$ For the same momentum and field, $r\propto\frac{1}{q}$. $\frac{r_H}{r_\alpha}=\frac{q_\alpha}{q_H}=\frac{2e}{e}=\frac{2}{1}$ $r_H:r_\alpha=2:1$

Concept radius of the circular path for equal momenta

Motion in Combined Electric and Magnetic Fields in past papers

13 questions from this chapter have appeared across 10 exam years.