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    Question

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

    a current I. If an infinitely long straight wire carrying the same current passes through the center perpendicular to the plane of the loop, what is the net force on the loop?
    A Attractive Correct Answer Incorrect Answer
    B Repulsive Correct Answer Incorrect Answer
    C Zero Correct Answer Incorrect Answer
    D Cannot be determined Correct Answer Incorrect Answer

    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
    Conceptual Understanding: The force on a current-carrying wire in a magnetic field is given by: F = I(L × B)
    • 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.
    Key Observations:
    • 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
    Due to symmetry:
    • 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.
    Net Result:
    • 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.

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