Question

A free proton and a free electron are placed in a uniform field. Which of the two experience greater force and greater acceleration?

Answer 1

Force on a charged particle in an electric field F=qEF=qE

For an electron or proton q=eq=e

∴F=eE∴F=eE

If m is the mass of the particle a=Fm=eEma=Fm=eEm

As electron is smaller in mass than that of a proton , the acceleration of the electron will be greater than that of a proton.

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Answer 2

In a uniform electric field, proton and electron experiences equal force and the acceleration of the electron is greater than proton.

• Let E be the uniform electric field.
• $m_{e}$ be the mass of the electron with charge 'e'.
• $m_{p}$ be the mass of the proton with charge 'p'.

Force experienced by the proton and electron:

• The force experienced by a charge 'q' in an electric field E is F = qE
• Force experienced by the electron $F_{e}$ = eE
• Force experienced by the proton $F_{p}$ = pE
• Since e and p are equal in magnitude $F_{e} = F_{p}$ .
• But e and p have opposite charges, therefore the forces are opposite in direction.
• Therefore, the proton and electron experience equal force (same magnitude but opposite direction) in a uniform electric field.

Acceleration experienced by the proton and electron:

• Mass and acceleration are inversely proportional to each other since F = ma
• Proton has a higher mass greater than the electron i.e;  $m_{p} > m_{e}$
• Therefore, acceleration of the proton is less than the acceleration of the electron in magnitude (opposite in direction) in a uniform electric field.