Ncert Exercises & Solutions

Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field 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: $(\frac{e}{m})_{1} + (\frac{e}{m})_{2} = 0$

d) Hint: Apply the concept of Lorentz force.

Step 1: For a given pitch,

P = \frac{2 πmvcos θ}{Bq}

\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}

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

So, it verifies answer (d).

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