Question

A free electron and a free proton are placed in an identical electric field. Which experience greater force? Which experience greater acceleration?  

Answer 1

Answer 2

In an identical electric field, both the free electron and the free proton experience the same force, but they experience different accelerations due to their different masses.

1. Force: The force experienced by a charged particle (electron or proton) in an electric field is given by the formula: F = q * E

where: F = Force on the charged particle q = Charge of the particle E = Electric field strength

Both the electron and the proton have charges of the same magnitude, but with opposite signs. The charge of an electron (e) is negative (-1.6 x 10^-19 C), while the charge of a proton (e) is positive (+1.6 x 10^-19 C). Since the magnitude of their charges is the same, the force on both the electron and the proton will be the same when placed in an identical electric field.

1. Acceleration: The acceleration experienced by a charged particle in an electric field is given by Newton's second law: a = F / m

where: a = Acceleration of the charged particle F = Force on the charged particle m = Mass of the charged particle

Here's where the difference lies: the mass of an electron is much smaller than the mass of a proton. The mass of an electron is approximately 9.11 x 10^-31 kg, while the mass of a proton is approximately 1.67 x 10^-27 kg.

Since the force is the same for both the electron and the proton, the acceleration of the electron will be much greater than the acceleration of the proton. In other words, the electron will experience a much larger change in velocity (acceleration) than the proton when subjected to the same electric field.

In summary:

• Both the free electron and the free proton experience the same force in the identical electric field.

• The free electron experiences a much greater acceleration than the free proton due to its much smaller mass.