Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?
1. Particles 1 and 2 are deflected towards the positively charged plate, hence it can be concluded that particles 1 and 2 are negatively charged.
2. Particle 3 is deflected towards the negatively charged plate hence it is positively charged.
The deflection of a particle is proportional to the charge to mass ratio (q: m) of the particle. We observe that particle 3 has maximum deflection, so it has the highest charge to mass ratio.
Explanation: Force on a particle in electric field
F = q × E …(1)
Where, q = charge on particle
E = magnitude of electric field
m × a = q × E …(2)
Where m = mass of particle
a = acceleration of particle
From equation (2)
⇒ 
The electric field in the given case is constant, hence we can write
⇒ 
…(3)
From the equation (3) we can conclude that acceleration of a charge particle with charge q and mass m in uniform electric field is proportional to the charge to mass ratio of the particle.