Question

If you place a free electron and a free proton in the same electric field, how will the forces acting on them compare? How will their accelerations compare? Their directions of travel?

Answer 1

Answer:

The forces (magnitude) would be the same; the electron would have a larger acceleration, and they will travel in opposite directions

Explanation:

- The magnitude of the force exerted on a charged particle by an electric field is

$F=qE$

where q is the magnitude of the charge and E is the electric field strength. Since the proton and the electron have same electric charge magnitude (e, elementary charge), they will experience the same force under the same electric field.

- The acceleration of a particle is given by

$a=\frac{F}{m}$

where F is the force exerted on the particle and m is the mass. Here, we said that the electron and the proton experience the same force F, however the mass of the proton is much larger (approx. 1800 times larger) than the mass of the electron, so the electron will experience a larger acceleration (because acceleration is inversely proportional to the mass)

- The direction of travel corresponds to the direction of the force. Since the proton is positively charged, the force exerted on it has same direction as the electric field; while since the electron is negatively charged, the force exerted on it has opposite direction to the electric field. Therefore, the two particles will travel into opposite directions.