Calculating magnitude of electric field at center of square

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SUMMARY

The discussion focuses on calculating the net electric field at the center of a square array of charges, specifically addressing the contributions from various charges. The correct formula for the electric field is derived as E = k[9q / (√2 * d)], factoring in the contributions from the charges positioned at the corners of the square. The x-component and y-component of the electric field are calculated using trigonometric functions, specifically E_x = (4k q^2/d^2)cos(45) and E_y = (4k q^2/d^2)sin(45). The participants emphasize the importance of correctly identifying charge contributions and resolving vector components accurately.

PREREQUISITES
  • Understanding of electric fields and Coulomb's law
  • Familiarity with vector resolution in two dimensions
  • Knowledge of trigonometric functions, particularly sine and cosine
  • Basic principles of charge interactions in electrostatics
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  • Study the principles of superposition in electric fields
  • Learn how to resolve vectors in two dimensions
  • Explore the concept of electric field lines and their representation
  • Investigate the effects of different charge configurations on electric fields
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Students studying electromagnetism, physics educators, and anyone seeking to understand electric field calculations in multi-charge systems.

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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