### Problem StatementFour infinitely long parallel wires carrying equal current \( I \) are arranged in such a way that, when looking at the cross-section, they are at the corners of a square, as shown in the figure below. Currents in wires at points \( A \) and \( D \) point out of the page, and currents at \( B \) and \( C \) point into the page. What is the magnetic field at the center \( P \) of the square?**Hint**: Set a 2-dimensional reference system with origin at \( P \). Use the formula for the magnetic field of an infinite wire and the superposition principle to find vector \( \mathbf{B} \).### Diagram ExplanationThe diagram depicts four points, labeled \( A \), \( B \), \( C \), and \( D \), located at the four corners of a square. Each side of the square is marked with length \( a \).- Points \( A \) and \( D \) have currents directed out of the page, represented by dots within circles.- Points \( B \) and \( C \) have currents directed into the page, represented by crosses within circles.At the center of the square is point \( P \), which is where the magnetic field is to be calculated. Each wire contributes to the magnetic field at the center based on their direction and magnitude of the current. ### Approach1. **Set up a coordinate plane**: Place the center \( P \) of the square at the origin.2. **Calculate magnetic effect**: Use the Biot-Savart Law or Ampere's Law for each wire to calculate the magnetic field contribution.3. **Apply the superposition principle**: Add the vector contributions of each wire to find the net magnetic field at the center \( P \).This setup and calculation method will allow you to determine the overall magnetic field at point \( P \).

Diagram Magnetic field is given by right hand rule.Magnetic field due to an infinite current carrying wire B=μ0I2πrSince all the wires carry the same current and are equidistant from the point, magnitude of magnetic field due to each wire is the same. From the figure, the horizontal component cancels each other whereas the vertical component adds up. Magnetic field at the center of the square. B=4BAsinθ=4μ0I2πrsin45°=4μ0I2πa22+a22sin45°=2μ0Iπ2a212=2μ0Iπa The net magnetic field is in the downward direction.

Answered: Four infinitely long parallel wires…