Four charges equal in magnitude form a square

[abm77]

Homework Statement

Four charges equal in magnitude of 20.0 microC are placed on the four corners of a square with side length 0.180m. Determine the electric field at the centre of the square.

(-q) ---------- (+q)
l l
l l
l l
(+q)----------(+q)

1 --------------- 2

3-----------------4

Formatting messes up the square but you get the point.

Homework Equations

ɛ = kq / r
ɛ = delta V / r

The Attempt at a Solution

I tried just adding up the combinations of each charge after calculating ɛ = kq / r for each. I didn't feel confident this was the correct way to do it, but no answer or solution was given.

ɛ1 = k(-0.00002) / 0.180 = -1.00 x 10^6
ɛ2&3&4 = k(0.00002) / 0.180 = 1.00 x 10^6

ɛ_total = ɛ1 + ɛ2 + ɛ3 +ɛ4
= -1.0 x 10^6 + 3(1.0 x 10^6)
= 2.0 x 10^6

 

[Orodruin]

Please show your work in more detail. There is no way we can tell if you did it right or wrong based on your post.

 

[abm77]

Please show your work in more detail. There is no way we can tell if you did it right or wrong based on your post.

Updated my solution to show my full work.

 

[Orodruin]

First of all, the distance from the charges to the center is not 0.18 m.

Second, the electric field is a vector. You cannot simply add the magnitudes of the fields from each charge. You need to add the field vectors as a vector addition, i.e., using both magnitude and direction.

 

[abm77]

First of all, the distance from the charges to the center is not 0.18 m.

Second, the electric field is a vector. You cannot simply add the magnitudes of the fields from each charge. You need to add the field vectors as a vector addition, i.e., using both magnitude and direction.

Right.

So I found the length to the centre from each corner to be 0.127m.

So if I were to add them as vectors would charge 2 and 3 cancel each other out, and I would be left to add charges 1 and 4 together since they are opposite charges?

 

[Orodruin]

Correct.

 

[abm77]

Correct.

Awesome thanks.

One last thing, is there a rule for determining which way the electric field vector is going? Like will it be towards 1 (-q) or 4 (+q)?

 

[Orodruin]

The field is pointing in the direction in which the force on a positive test charge at the given position would point. Thus, the field from a negative charge points towards it (the negative charge) and the field of a positive charge away from it (the positive charge).