What is the relationship between Electrostatic force and Electric field?

[Achilles]

Let us say between a proton and electron at a small distance d. They are opposite charges so they feel an electrostatic force of attraction. What about electric field. Do I just draw the lines from positive to negative for electric field?

[Sensei]

Quote

What is the relationship between Electrostatic force and Electric field?

Force is in Newtons unit.

[math]F=k_e\frac{q_1 q_2}{r^2}[/math]

Electric field is in V/m unit, or N/C unit:

[math]F=q_1 E[/math]

[math]E=k_e\frac{q}{r^2}[/math]

Vector version of equation:

[math]\vec{E(r)}=k_e\frac{q}{r^2}[/math]

Edited August 17, 2018 by Sensei

[MigL]

That is the 'classical' way of looking at things.
the electric field provides the means, or enables, the 'action-at-a-distance' of the electrostatic force.

Quantum field theory turns this upside down.

[studiot]

2 hours ago, Achilles said:

What is the relationship between Electrostatic force and Electric field?

Let us say between a proton and electron at a small distance d. They are opposite charges so they feel an electrostatic force of attraction. What about electric field. Do I just draw the lines from positive to negative for electric field?

I note you stated electrostatic force and field.
I further assume you are extending your earlier enquiry as to why the electron does not 'fall' 'into the nucleus.

I was mulling over a reply to this when you posted this new thread.

 

OK so Sensei is totally correct, those are the static equations.

But I think they are of no use to you because you are (or should be) looking for and equation of motion.

Earnshaw's theorem (1842) states that any system of more than one charge must be in motion (and you have two in your system).

This and the classical consideration leads to an answer to your earlier thread and this one, if you are interested.

The way to handle this is not to consider forces but to consider potentials and develop an equation of motion of one charge under the influence of the field of the other.

This is done both in classical mechnaics and the Schrodinger equation (and also the Dirac relativistic equation).

Do you wish to take this further?

[swansont]

3 hours ago, Achilles said:

Let us say between a proton and electron at a small distance d. They are opposite charges so they feel an electrostatic force of attraction. What about electric field. Do I just draw the lines from positive to negative for electric field?

The electric field from a particle is the force per unit charge that a positive test charge would feel at a location. Force is a vector, so for two charges you would use the vector sum of the field of each charge.