# Scalar potential in EM and Newton's Law

luxiaolei
Hi,all, problem is:

in Electromagnetism, we introduced a scalar potential psi, such that:

and In newton's law, there is also a scar potential U, such that:

My question is, one is the gradient of a scalar field give a field and a force???!!

Can anyone help me with understanding this? That would be great, and many thanks in advance!

Mentor
2021 Award
The field is just a force scaled by charge. It is the same relationship as e.g. the gravitational field and weight.

luxiaolei
The field is just a force scaled by charge. It is the same relationship as e.g. the gravitational field and weight.

@DaleSpam; thanks for replay. I am very interested in your answer, however, I am not quite understood it. Would you explain it more? thanks

Can I say,

Electric force = -grad psi = E

or

Gravitation field = -grad U = F

if they are the same.

Mentor
2021 Award
Yes. For example, if U = kCc/r then you get the electric force, if psi = kC/r then you get the electric field. Similarly, if U = GMm/r you get the gravitational force, if psi = GM/r then you get the gravitational field.

luxiaolei
Yes. For example, if U = kCc/r then you get the electric force, if psi = kC/r then you get the electric field. Similarly, if U = GMm/r you get the gravitational force, if psi = GM/r then you get the gravitational field.

Thanks a lot!! Cleared my mind!