An electron, a positron and a proton enter into a uniform magnetic field B at right angles to the direction of the field. If they have same velocity, identify the correct relation of the radii of the circular paths traced by these particles in the magnetic field.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → rproton > relectron = rpositron
A charged particle moving at right angles to a uniform magnetic field moves in a circle, with the magnetic force providing the centripetal force.
\( \displaystyle qvB = \frac{mv^{2}}{r} \;\Rightarrow\; r = \frac{mv}{qB} \)
All three particles have the same speed, move in the same field and carry a charge of the same magnitude e, so r is proportional to m.
\( m_{\mathrm{electron}} = m_{\mathrm{positron}} \lt m_{\mathrm{proton}} \)
\( r_{\mathrm{proton}} \gt r_{\mathrm{electron}} = r_{\mathrm{positron}} \)
The electron and positron move on circles of the same radius but in opposite senses, because their charges are opposite.