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.

Answer 2

The forces acting on proton and electron is same, acceleration of electron is greater and  the directions of travel of them is opposite to each other.

What is electric force?

Electric force is the force of attraction of repulsion between two bodies.

Due to an electric field, the electric force on a charged particle can be given as,

$F=qE$

Here, (q) is the charge on the body and (E) is the electric field.

• Charge on the electron and proton-

It is known that the charge on an electron is equal and opposite. Hence, the if the free electron and a free proton are placed in the same electric field, then the electric force acting on them will be the same.

• Accelerations of electron and proton-

As the acceleration of a body is the ratio of force acting on a body to the mass of it. Here, the force is same, but the mass of proton is greater than the mass of electron.

Thus, by the above formula, the electron will have greater value of acceleration.

• Their directions of travel-

It is known that the proton is positively charged, and the electron is negatively charged. This opposite charge, force them to travel in opposite direction to each other.

Hence, the forces acting on proton and electron is same, acceleration of electron is greater and  the directions of travel of them is opposite to each other.

Learn more about the electric force here;

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