Question

Two charged particles traverse identical helical paths in a completely opposite sense in the presence of a uniform magnetic field $\overrightarrow{B}=B_0\hat{k}$. The correct statement for the above is

• A. They must have equal charges.
• B. They have equal $z-$component of moments.
• C. The charge to mass ratio's satisfy, ${\left(\frac{q}{m}\right)}_1+{\left(\frac{q}{m}\right)}_2=0$
• D. They necessarily represent a particle-antiparticle pair.

Answer 1

The correct option is C The charge to mass ratio's satisfy, ${\left(\frac{q}{m}\right)}_1+{\left(\frac{q}{m}\right)}_2=0$

The pitch of the helix, (i.e., linear distance travelled in one rotation) will be given by

$P=Tv\cos \theta$

$\Rightarrow P=\frac{2\pi m}{qB}v\cos \theta$

For a given pitch $P$ corresponding to a charge particle, we have

$\frac{q}{m}=\frac{2\pi v\cos \theta }{PB}=\text{constant}$

In this problem, charged particles traverse identical helical paths in a completely opposite sense.

So, $\frac{q}{m}$ for two particles should be the same and of opposite sign.

So, ${\left(\frac{q}{m}\right)}_1+{\left(\frac{q}{m}\right)}_2=0$

Hence, option (c) is the correct answer.