Net Electric Field at the center of a square

[kemcco1955]

Homework Statement

What net electric field do the particles of problem #1 produce at the square's center? Problem number one has a square with edge lengths of 24.00cm and charges of q1==8.0e-6C, q2=-8.0e-6C, q3=-8.0e-6, and q4=+8.0. He wants the answer for the electric field in component form(Etotal= N/C x + N/Cy. I do not know how to find electric field when using different components.


2. Homework Equations
Ecenter=kq/r^2


3. The Attempt at a Solution
I know that q1 and q3 cancel/ equal zero because they are both negative and on the diagonal from one another. The vector for q2 points away from the charge and the vector for q4 points toward the charge. I find E2 using (8.99e9)(-8e-6)/.1697^2. And for E4 I get the same but with an opposite sign. The r it got to be .1697 m by taking the sqrt of .24^2+.24^2 =.3394/2=.1697. The angel, I think is 45 degrees. I am having difficulty finding how to get the E total into components I know that you can take an answer and multiply it by cos45 and sin45(which are the same), but I don't know how to set up the vectors to solve...I hope that makes some since...I am very confused.

 

[mark726]

To find the net electric field at the center of the square, you can use vector addition. The formula for the net electric field at a point due to multiple charges is:

E = k * (q1/r1^2 + q2/r2^2 + q3/r3^2 + q4/r4^2)

Where k is the Coulomb's constant, q1, q2, q3, q4 are the charges, and r1, r2, r3, r4 are the distances from each charge to the point where you want to find the electric field.

In this case, since q1 and q3 cancel out, you only need to consider q2 and q4. The distance from each of these charges to the center of the square is the same (since the square is symmetrical), so you can use the same value for r for both q2 and q4.

To find the components of the electric field, you can use the following formulas:

Ex = E * cosθ
Ey = E * sinθ

Where θ is the angle between the electric field and the x-axis.

To find the angle θ, you can use trigonometry. The angle between the electric field and the x-axis is the same as the angle between the vector from the charge to the center of the square and the x-axis. This angle can be found by using the inverse tangent function:

θ = tan^-1(y/x)

Where y is the vertical distance from the charge to the center of the square and x is the horizontal distance.

Once you have the angle θ, you can plug it into the above formulas to find the components of the electric field.

I hope this helps clarify how to find the components of the electric field in this problem. Let me know if you have any further questions.