# An A-particle and a Proton of the Same Kinetic Energy Are in Turn Allowed to Pass Through a Magnetic Field Vecb Acting Normal to the Direction of Motion of the Particles. - Physics

#### Question

Sum

An a-particle and a proton of the same kinetic energy are in turn allowed to pass through a magnetic field vec"B", acting normal to the direction of motion of the particles. Calculate the ratio of radii of the circular paths described by them.

#### Solution

Mass of alpha particle = m_a

Charge on alpha particle = q_α

Velocity of alpha particle = V_α

Mass of a proton = mp

Charge on a proton = q

Velocity of proton = vp

Since the KE of alpha particle and proton are equal.

∴ 1/2m_αν_α^2 = 1/2m_p.ν_p^2

⇒ (m_αν_α)^2/m_α = (m_p.ν_p)^2/m_p ⇒ (m_αν_α)/(m_p.ν_p) = (m_α/m_p)^(1/2)

Radius of the circle = R = (mν)/(qB)

Therefore, ratio of radii of alpha particle to proton

= R_α/R_p = (m_α.ν_α)/(q_αB).(q_pB)/(m_p.ν_p) = (m_α/m_p)^(1/2).q_p/q_α

Using  m_alpha/m_p = 4 and q_p/q_alpha = 1/2

∴ R_alpha/R_p = (4)^(1/2)(1/2) = 1

Concept: Introduction of Magnetism
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