Two charged particles traverse identical helical paths in a compl… - Vidyadip

MCQ

Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field $B = B_0 \hat k$ .

A
They have equal $z-$ components of momenta
B
They must have equal charges
C
They necessarily represent a particle, antiparticle pair
✓
The chrge to mass ratio satisfy ${\left( {\frac{e}{m}} \right)_1} + {\left( {\frac{e}{m}} \right)_2} = 0$

✓

Answer

Correct option: D.

The chrge to mass ratio satisfy ${\left( {\frac{e}{m}} \right)_1} + {\left( {\frac{e}{m}} \right)_2} = 0$

d
For given pitch, $d$ corresponds to charged particle, we have

$\frac{\mathrm{q}}{\mathrm{m}}=\frac{2 \pi \mathrm{v} \cos \theta}{\mathrm{B}}=\mathrm{constant} \Rightarrow\left(\frac{\mathrm{e}}{\mathrm{m}}\right)_{1}+\left(\frac{\mathrm{e}}{\mathrm{m}}\right)_{2}=0$

Note Consider $e$ in place of $\mathrm{q}$ in solution.

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