Electric field when there are 3 charges

[awertag]

Homework Statement

A point charge q = +2.8 µC is placed at each corner of an equilateral triangle with sides 0.19 m in length.
(a) What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle?

Homework Equations

E=kq/r^2
k=9e9
all q's are q=2.8e-6 C

The Attempt at a Solution

so i solved for the three E fields.
E1=9.3126e5 E2=2.7922e6 E3=2.7922e6

well, i know that they all point away from the positive charges and therefore at the point.
But I can't seem to combine them correctly. I have to use i and j vectors, right?

any good help will be greatly appreciated!

--aweg

 

[Piyu]

I think its just the e field of the point charge opposite it, since the E field of the 2 other charges are laying on the same line directly opposite hence should cancel out.

If we take out the charge opposite the midpoint test charge, a charge placed in the middle of 2 equal charges should experience zero net force. Hence by superposition, they should cancel out too in this case.

On reading ur question and answer, i think there's abit of confusion here, there's A point charge at each corner? I am guessing it is so because of the way the question was asked(they said EITHER(any) of the midpoints of the 3 lines.)

 

[awertag]

yes, there are three charges, one at each corner. And that makes sense, i don't think i tried that yet.

 

[awertag]

ok so then in the center of the triangle, the E field would be zero?

 

[Piyu]

Yep, logically speaking.

And you can easily prove this by assuming one charge exerts X amount of force on a test charge in the middle and use equilateral triangles to sum up the forces. Should give you zero.

 

[awertag]

Well, thanks very much for the help and have a great day! :)