Electric field at the center of a square homework

In summary, the electric charge is distributed uniformly along each side of a square, with two adjacent sides having positive charge and the other two sides having negative charge. When calculating the x-component of the net electric field at the center of the square, the x-components of the electric fields from the positive and negative charges should be in the same direction and equal in magnitude. Simply doubling the equation for an electric field does not work in this case because the sides of the square are charged rods and not point charges. The correct answer is -\frac{\sqrt{2} \cdot Q}{\pi \cdot a^2 \cdot \epsilon_0}.
  • #1
erik-the-red
89
1
Question:

Electric charge is distributed uniformly along each side of a square. Two adjacent sides have positive charge with total charge + Q on each. Each side of the square has length a.

Image at bottom.

Part A:

Suppose the other two sides have negative charge with total charge - Q on each. What is the x-component of the net electric field at the center of the square? Give your answer in terms of Q, a, and epsilon_0.

The electric field at the origin would point away from the positive charge and point towards the negative charge. The x-components would both be in the -x direction and equal in magnitude.

I thought all I had to do was double the equation for an electric field with Q as the charge and (.5a) as the distance.

My answer was - (2)*(Q) / (Pi* a^(2) * (epsilon_0).

Because this is a Mastering Physics question and I was close, my feedback was "Your answer is off by a multiplicative factor."

What did I do wrong?
 

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  • #2
I thought all I had to do was double the equation for an electric field with Q as the charge and (.5a) as the distance.
You can't just double it. Since each side is a charged rod, you will have to find the electric field a distance .5a away from a charged rod. What you did would work if it were a point charge.
 
  • #3
I exceeded my attempts (five) on the first part. It was the same as the second part, so I ended up getting 3/4s of the points.

I don't understand why the answer is [tex]-\frac{\sqrt{2} \cdot Q}{\pi \cdot a^2 \cdot \epsilon_0}[/tex].
 

1. What is the formula for calculating the electric field at the center of a square?

The formula for calculating the electric field at the center of a square is E = kQ/a^2, where E is the electric field, k is Coulomb's constant, Q is the total charge on the square, and a is the length of one side of the square.

2. How do you determine the direction of the electric field at the center of a square?

The direction of the electric field at the center of a square can be determined using the right-hand rule. If the charges on the square are positive, the electric field points away from the center, and if the charges are negative, the electric field points towards the center.

3. What factors affect the strength of the electric field at the center of a square?

The strength of the electric field at the center of a square is affected by the total charge on the square, the distance between the charge and the center of the square, and the size of the square. Increasing the charge or decreasing the distance will increase the strength of the electric field, while increasing the size of the square will decrease the strength of the electric field.

4. Can the electric field at the center of a square be zero?

Yes, the electric field at the center of a square can be zero. This occurs when the total charge on the square is zero or if the charges on opposite sides of the square are equal and cancel each other out.

5. How is the electric field at the center of a square related to the electric potential?

The electric field at the center of a square is directly proportional to the electric potential at that point. This means that as the electric field increases, the electric potential also increases. The relationship is described by the equation E = -∇V, where E is the electric field and V is the electric potential.

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