What is the Net Electric Field at the Center of a Square with Four Charges?

In summary, the conversation discusses the placement of four point charges, two positive and two negative, at the corners of a square with side length a. The question asks for the magnitude of the net electric field at the center of the square in terms of q and a. The equations used are E = k (q / r^2) with k = 9.0 * 10^9, and the distance from the center to one of the charges is a/(2^1/2). The x-components cancel out, leaving only the y-components. The final answer is 4 * 9.0 * 10^9 (2q / a^2) * (1 / (2^1/2)).
  • #1
spiffmonkey1
2
0

Homework Statement



A point charge is placed at each corner of a square with side length a. The charges all have the same magnitude q. Two of the charges are positive and two are negative, as shown in the following figure.

The two positive charges are on top and the two negative charges are on the bottom

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of q and a?


Homework Equations



E = k ( q / r^2), k = 9.0*10^9

The Attempt at a Solution



The distance from the middle to one of the charges a/(2^1/2)

The x-components cancel out, leaving only the y-components.

The electric field due to one of the charge to my guess is-
E1sinω = 9.0*10^9 ( 2q / a^2 ) * (1/ (2^1/2))

I assumed that each charge exerts the same electric field so the answer would\ be
4 * 9.0*10^9 ( 2q / a^2 ) * (1/ (2^1/2))

I am not sure what I did wrong.

Thanks so much
 
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  • #2


Nevermind, masteringphysics believes that k != 9.0 * 10^10 , correct answer above

Mod close thread please.
 

FAQ: What is the Net Electric Field at the Center of a Square with Four Charges?

What is the definition of "net electric field"?

The net electric field is the sum of all electric fields at a specific point in space, taking into account both magnitude and direction.

How is the net electric field at the center of a square calculated?

The net electric field at the center of a square is calculated by adding the individual electric fields from each point charge at the center, taking into account the distance and direction of each charge.

What factors affect the magnitude of the net electric field at the center of a square?

The magnitude of the net electric field at the center of a square is affected by the number of charges, their magnitudes, and their distances from the center. Additionally, the orientation of the square and the presence of any external electric fields can also impact the net electric field.

How does the magnitude of the net electric field at the center of a square change if the distance between the charges is increased?

If the distance between the charges is increased, the magnitude of the net electric field at the center of the square will decrease. This is because the electric field strength decreases with distance according to the inverse square law.

Can the net electric field at the center of a square ever be zero?

Yes, the net electric field at the center of a square can be zero if the magnitudes and distances of the charges are equal and opposite, cancelling out each other's electric fields. This is known as a neutral equilibrium point.

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