An electron, a proton and an alpha particle having the same kinetic energy

• Magnetism

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_e, r_p, r_α respectively in a uniform magnetic field B. The relation between r_e, r_p, r_α is :

1. r_e < r_p = r_α
2. r_e < r_p < r_α
3. r_e < r_α < r_p
4. r_e > r_p = r_α

Answer

Radius of circular path in magnetic field is given by

R = √(2Km)/qB

where

• K = kinetic energy of particle
• m = mass of particle
• q = charge on particle
• B = magnetic field intensity
• R = radius of path

R ∝ √m/q

As m_e < m_p

r_e < r_p

r_α ∝ √(4m_p)/ 2q_p

r_α ∝ √(m_p) / q_p

r_α = r_p

The correct option is A.