Question

A proton and a deuterium nucleus having certain kinetic energies enter in a uniform magnetic field with same component of velocity in the direction of magnetic field. Which of the following is correct?​

Answer 1

A proton and a deuterium nucleus having certain kinetic energies enter in a uniform magnetic field with same component of velocity in the direction of magnetic field.

Which of the following is correct ?

1. which particle has greater pitch depends on the fact which particle has greater component of velocity perpendicular to magnetic field.
2. Deuterium nucleus has greater pitch of helical path.
3. proton has greater pitch of helical path.
4. Both particles have same pitch of helical path.

Pitch is horizontal distance between two consecutive circles. Pitch of a charged particle in magnetic field is given by, $\bf s=\frac{2\pi mvcos\theta}{qB}$

here, $vcos\theta$ shows the pitch of the particle depends on the horizontal component of the velocity. so the option (1) is incorrect.

given, A proton and a deuterium nucleus having certain kinetic energies enter in a uniform magnetic field and the components of velocity of protons and deuterium in the direction of manetic field are same.

∴ velocity and magnetic field remain constant.

also we know charge on proton = charge on deuterium

so charge also remains constant.

∴ here the pitch only depends on mass of particle.

∵ mass of deuterium = 2 × mass of proton

∴ pitch of deuterium = 2 × pitch of proton

Therefore deuterium has greater pitch in the magnetic field. option (2) is correct.