Find the magnetic field at the center of the square

In summary, the question asks for the magnetic field at the center of a square formed by four parallel wires carrying currents in opposite directions. Using the right hand rule, the magnetic field will point to the left. To find the magnitude, each wire must be treated as a line current and added together, taking into account their different directions. There may be a shortcut due to the symmetry of the setup.
  • #1
musicmar
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Homework Statement


Four long, straight wires parallel to the z axis pass through the points (±7.5 cm, ±7.5 cm) at the corners of a square in the x-y plane. Each carries a current of 2.5 A, with the upper two currents in the -z direction and the lower two in the +z direction. Find the magnetic field at the center of the square.

The Attempt at a Solution



Defining out of the page as the positive z-axis:

x x

. .

Using the right hand rule, the magnetic field will point to the left.

I don't really know how to find the magnitude, though. Do I treat each as a line current and add them together?

Thank you.
 
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  • #2
Do I treat each as a line current and add them together?
Yes. Each will be in a different direction so the adding will be just a little complicated. Lots of symmetry, though - maybe you will see a shortcut.
 

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

The formula for calculating the magnetic field at the center of a square is B = μ0 * I / (2 * a), where B is the magnetic field strength, μ0 is the permeability of free space, I is the current flowing through the square, and a is the length of each side of the square.

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

The direction of the magnetic field at the center of a square is perpendicular to the plane of the square, and follows the right-hand rule. If you point your thumb in the direction of the current, your fingers will curl in the direction of the magnetic field.

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

The strength of the magnetic field at the center of a square is affected by the current flowing through the square, the permeability of free space, and the length of each side of the square. Additionally, the distance from the center of the square to the measuring point can also affect the strength of the magnetic field.

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

No, the magnetic field at the center of a square cannot be zero. This is because the current flowing through the square creates a magnetic field that is perpendicular to the plane of the square, and this field will always have a non-zero magnitude.

5. How does the magnetic field at the center of a square differ from the magnetic field at other points on the square?

The magnetic field at the center of a square is unique because it is equidistant from all sides of the square, resulting in a symmetrical distribution of the magnetic field. In contrast, the magnetic field at other points on the square may vary in direction and strength depending on their distance from the current-carrying sides of the square.

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