A wire loop in the shape of a square of side a carries

Solution

Given:

• A square current loop of side a carrying current I
• An infinitely long straight wire, also carrying current I, passes perpendicularly through the center of the square loop
• Both currents are in the same direction
• We are to find the net force on the loop

• The infinitely long wire creates a magnetic field around it.
• The square loop is placed symmetrically around the wire (the wire passes through its center).
• Each segment of the loop experiences a magnetic force due to the field created by the central wire.

• The magnetic field around the wire follows circular paths (right-hand rule).
• The force on each side of the loop depends on:
• Direction of the magnetic field at that location
• Direction of current in that segment

• The forces on opposite sides of the square loop are equal in magnitude but opposite in direction.
• Therefore, horizontal and vertical components of forces on opposite sides cancel each other out.

• While individual sides of the loop experience non-zero forces, the vector sum of all forces is zero.
• Hence, the net force on the square loop is zero.