Calculating magnitude of electric field at center of square

AI Thread Summary
The discussion focuses on calculating the net electric field at the center of a square array of charges, specifically addressing the contributions from different charge magnitudes. The initial approach incorrectly ignored the influence of the -5q charge and misidentified the components of the electric field. Corrections were suggested, including properly accounting for the charge contributions and adjusting the distance terms in the equations. The need to resolve the electric field into x and y components was emphasized, along with calculating the resultant magnitude. Overall, the conversation highlights common pitfalls in electric field calculations involving symmetrical charge distributions.
Physics2341313
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Homework Statement



Find the magnitude and direction of net electric field at the center of the square array of charges. Find E_x and E_y

The square array of charges http://postimg.org/image/4gf94ymmf/

The Attempt at a Solution


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My attempt at drawing in the force vectors http://postimg.org/image/mae0fm1d9/ . Now the +3q and +q's should contribute a net of zero to the electric field and they can be ignored. So, we have E = k [ -2q^2 / d^2 + q^2/d^2 + 5q^2/d^2] = 4k q^2/d^2

Taking the x-component of the field we have
E_x = (4k q^2/d^2)cos(45)

the y-component:
E_x = (4k q^2/d^2)sin(45)

This isn't right or I would not be posting here... so what am I doing wrong? I'm really not understanding how to do these types of problems for net fields in squares. Have I even drawn the vectors correctly?
 
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Physics2341313 said:
k[−2q 2 /d 2 +q 2 /d 2 +5q 2 /d 2 ]=
You're missing a term.
 
The missing term is the -5q charge, yes? So it should be
E=k[−2q/(\sqrt2 * d)+q/(\sqrt 2 * d) + 2(5q/(\sqrt 2 * d))= k[9q / (\sqrt 2 * d)]

Also, changed q^2 to q since this is the electric field not force... silly mistake, and the bottom term should be \sqrt 2 * d instead of d^2?

This is still incorrect is not? I'm really not seeing what I'm missing here.
 
Methinks that should do almost do it (dumped the picture, so I'm going by memory); the "two" and "one" are both on axes? In which case "d."
 
Bystander said:
Methinks that should do almost do it (dumped the picture, so I'm going by memory); the "two" and "one" are both on axes? In which case "d."
Ah fair point forgot about those being strictly on the x-axis, so need to fix that then resolve into E_x and E_y for the respective terms and then take the square root of those squared for the magnitude.
 
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