A deutron and an $α$-particle moving with the same velocity enter into a uniform magnetic field acting normal to the plane of their motion. The ratio of the circular paths described by the deutron and $α$-particle is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) - 1 : 1
The radius (r) of the circular path of a charged particle with velocity (v) and magnetic field (B).
$r=\frac{mV}{qB}$
where,
q → charge of particle
v → velocity of particle
$r_{deuteron}=\frac{m_{deuteron}V}{q_{deuteron}B}=\frac{2m_pV}{eB}$
$r_{α-particle}=\frac{m_{α}V}{q_{α}B}=\frac{4m_pV}{2eB}=\frac{2m_pV}{eB}$
$\frac{V_{α}}{d_{deuteron}}=\frac{\frac{2m_pV}{eB}}{\frac{2m_pV}{eB}}=1$