The Field of an Electric Dipole

[Violagirl]

Homework Statement

Consider an electric dipole in the attached document. At point P, the fields E₊ due to q+ and E_- due to q- are:

E₊ = kq/(r-a)², E_- = -kq/(r+a)²


Then total field at P is:

E = E₊ + E_- = kq [ 1/(r-a)² - 1/(r+a)²] y-hat

Homework Equations

See question 1.

The Attempt at a Solution

So this post is just trying to comprehend the example problem above. I don't believe I'm fully understanding electric field. In the problem above, they have a point P without a charge given. They say that the impact of the electric field of +q occurs at a distance of r-a which makes sense if P is a positive charge. But then for -q, it takes place at a distance of r+a. What I don't understand for this, shouldn't it take place at a distance of 2a+r? It seems like it'd be a distance of 2a from Point P. Or are we considering that the electric field is moving towards -q? I'm not sure I understand this problem...

 

[marcusl]

P is just the label for a point of interest where you are being asked to evaluate the electric field. There's no charge there because it's just a location--the location where an observation of the 2 charges will be made.

Point P is located a distance r from the origin in your diagram. Since the + charge is a distance a from the origin in the same direction, the separation between +q and P is r-a. The - charge is located at -a, which is a distance a from the origin in the direction opposite from P. The distance from +q to P must be r+a as states. So far this is just simple use of a ruler.

Does this help?

 

[Violagirl]

Yes it does, thank you very much!