Understanding Electric Potential: How Does Charge Density Affect Potential?

[SchruteBucks]

This is more of a question about a concept than the actual homework problem. The homework problem gives diagrams of rods with varying charge densities, but there's one important concept I don't yet understand, and it's stopping me from moving on in the problem.

My question is even more simple though...

Would the electric potential (at each point P) in my two diagrams be the same?

(+q)-----P-----(+q)

P-----(+2q)

i.e., do the positions of the charges affect the electric potential at that point or is the electric potential solely dependent on the charge and its distance from the point?
I'm leaning towards the latter and that the electric potential IS the same based on the fact that its scalar and direction shouldn't matter (?) but I really have no idea.
Any help would be VERY much appreciated!

 

[technicolour1]

Well, since potential is a scalar, the equation representing the first diagram would be:

V = (keq/r + keq/r) = 2keq/r = ((ke/r)(2q)) = (ke2q/r)

The equation representing the second scenario would be

V = (ke2q/r)

This works only because they are scalar.

Also, love the username.

 

[gneill]

Yes, those two potentials are the same. The contribution of a charge to a potential at a point depends upon the magnitude of the charge and the distance from that charge. Potential obeys the superposition principle, so you can add the individual contributions.

You could also satisfy yourself that they are the same by constructing and solving the appropriate integration...

$$\Delta V_E = -\int_C \vec{E} \cdot \vec{dL}$$

Where the integration is a line integral along a path from a point of zero potential (usually taken to be some point off at infinity) to the point in question.

 

[SammyS]

This is more of a question about a concept than the actual homework problem. The homework problem gives diagrams of rods with varying charge densities, but there's one important concept I don't yet understand, and it's stopping me from moving on in the problem.

My question is even more simple though...

Would the electric potential (at each point P) in my two diagrams be the same?

(+q)-----P-----(+q)

P-----(+2q)

i.e., do the positions of the charges affect the electric potential at that point or is the electric potential solely dependent on the charge and its distance from the point?
I'm leaning towards the latter and that the electric potential IS the same based on the fact that its scalar and direction shouldn't matter (?) but I really have no idea.
Any help would be VERY much appreciated!

You seem to be asking:

Is the electric potential the same for the following two situations?

1). The point at with you are find the electric potential is a distance, d, from two distinct point charges, each with charge q.

2). The point at with you are find the electric potential is a distance, d, a single point charge having charge 2q.​

The answer is, definitely yes.

 

[SchruteBucks]

WOW great responses, and fast too...this makes my homework MUCH easier! I'm glad all of you understood what I was trying to ask, and the answers couldn't have been any clearer! I even have some useful equations to use now. EXTREMELY helpful, I can't thank you enough!