Electric potential vector or scalar sum?

[rickywaldron]

I'm having trouble fully understanding what electrical potential means. If there are two point charges of opposite signs and a point charge somewhere around them, we simply add the two voltages separately? Not as a vector sum?

Also the concept of negative potential, does this mean that the force is directed towards the charge as opposed to away?

 

[Simon Bridge]

It's the amount of work needed to get a unit positive charge to that spot.
It is a scalar sum because work is not a vector quantity.
However, scalars are allowed to be negative.

The minus sign on the potential does not indicate direction.

A negative potential is attractive to a positive charge and repulsive to a negative charge.
I think you need to review the relationship between potential, potential energy, and work.

 

[rickywaldron]

Ok, so if I move a proton to the mid point between 2 point charges -10 and +6 it will gain energy from the force it had to use to move against the positive charge, but it will lose even more evergy than this from the negative charge attracting it? Hence the electric potential energy and voltage is negative?

 

[Simon Bridge]

That's pretty much it. Your example, you didn't specify the units for charges. If the proton (charge +e) were (distance x) mid-way between a charge of +6e and -10e then the net potential is given by:

$$V=\frac{6ke}{x}-\frac{10ke}{x} = -\frac{4ke}{x}$$

You should be moving away from a force approach to motion and more towards using energy instead. There will be a transition where you will find forces easier to visualize.

The proton is acted on by a net force, the total work is associated with this net force via W=F.d (note that force and displacement are vectors?)

You can expand the F term into each individual force, and each force into components along and perpendicular to the displacement, getting a big sum ... each term of the sum will, itself, be work (energy) and you'll see how some of the terms will be positive and some negative. Thinking in terms of energy becomes very convenient later.

If you imagine a system of two charges, and you move a proton to a position where one charge contributes +6V and the other contributes -10V then the proton, by virtue of being in that position, has -4eV potential energy[1].

If you then move it into a position where is has -7eV potential energy then it has gained 3eV kinetic energy. If you wanted to return it to where it has 0eV potential energy, you'd have to give the proton 7eV of kinetic energy (somehow) to get it there.

You can imagine the same thing with gravity ... gravitational potential energy [close to the Earth is approximated by] mgh, where h is measured upwards from the ground ... this can be a negative number, for instance, if your mass is down a hole.

For this reason, regions of negative potential or often called "potential wells". (Regions of positive potential are called "barriers".)

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[1] spot the units ... eV = electron-volt: convenient for protons which have the charge of a single electron only positive. I could have expressed potential as J/e instead of Volts which is J/C and then expressed energies as Joules.

 

[Nickie]

The electric potential is a scalar quantity, meaning it has magnitude but no direction. It represents the amount of work needed to move a unit charge from one point to another in an electric field. When there are multiple point charges, the electric potential at a point is the sum of the individual potentials due to each charge, as long as we are dealing with a static situation.

When considering the forces between charges, we use the electric field, which is a vector quantity. The direction of the electric field at a point is the direction of the force that a positive charge would experience at that point. So, while the electric potential itself is not a vector, the electric field is.

In terms of negative potential, this does not necessarily mean that the force is directed towards the charge. It simply means that the work needed to move a unit charge from that point to infinity is negative, indicating that the electric field is doing work on the charge. This can happen in cases where the charge is moving in the opposite direction of the electric field, for example.