Electric field of two point charges

[black_hole]

Homework Statement

Two point charges Q and -Q are separated by a distance d. The point p forms an equilateral triangle with the two charges of side length d. Find the magnitude and direction of the electric field at point p. What is the electric potential at P? Then, a charge of 2Q is placed at P. What is the potential energy of this charge?

Homework Equations

F = qE
V = ∫E dx
U = qV

The Attempt at a Solution

I was thinking the field at P would be zero bc the negative and positive charges would have a cancelling effect but that doesn't seem right when I think of a field picture. But once I figure out that I think I can figure out the potential and the potential energy of 2Q. To figure out the potential at point p would I integrate with respect to r or x?

 

[Mindscrape]

Well, you're kind of right. Draw out the picture and you'll find they cancel in one direction, but not completely in all directions, as you suggested.

 

[black_hole]

ok, so do they cancel out in the x direction, but not in the y is that right? In that case is it Ey = kQ/(d/2)^2 ? and on that notes, should I also integrate along the y direction to find the potential at p?

 

[Mindscrape]

I think you may have gotten the E-field convention mixed up. Positive charges produce vectors away from it, and negative charges produce vectors towards. No integration needed, and make sure you've done your trig right. You're getting there.

 

[black_hole]

Now I'm confused...If I were to draw it out, the electric field would be going from the positive charge down to the negative charge in a sense right? What does that mean for point p?

 

[Mindscrape]

So your point p is positive "test charge." The electric field is basically how forces would look if you placed a grid of "test charges" all over the place. So say Q is on the left and -Q is on the right. Q gives in E-field on p that's up and to the right, while -Q gives an E-field down and to the left. Superposition means that you simply add the two together, so you'd have an E-field solely to the right.

Hah, actually, I just noticed, I never asked for your original so you could have been right if you were thinking of having the charges aligned vertically and I just assumed we were placing the charges horizontally.

 

[black_hole]

Well, but the two charges Q and point p form an equilateral configuration. I know electric fields are superposable but in this configuration, I'm worried about direction