Ncert Exercises & Solutions

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

1.	They have equal $z-$ components of momenta.
2.	They must have equal charges.
3.	They necessarily represent a particle-antiparticle pair.
4.	The charge to mass ratio satisfy: $\left( \dfrac{e}{m} \right)_{1} + \left( \dfrac{e}{m} \right)_{2} = 0$

d) Hint: Apply the concept of Lorentz force.

Step 1: For a given pitch,

P = \frac{2 πmvcos θ}{Bq}

$P = \frac{2 πmvcos θ}{Bq}$ ,

\frac{q}{m} = \frac{2 πvcosθ}{BP} [θ

$\frac{q}{m} = \frac{2 πvcosθ}{BP} [θ$ = angle of the velocity of a charged particle with x-axis]

If the motion is not helical,

θ = 0^{o}

$θ = 0^{o}$ .

Step 2: As the path of both the particles is identical and helical but of opposite direction in the same magnetic field, so by the law of conservation of momenta:

(\frac{e}{m})_{1} + (\frac{e}{m})_{2} = 0

$(\frac{e}{m})_{1} + (\frac{e}{m})_{2} = 0$

So, it verifies answer (d).

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