The resultant force on the current loop P Q R S due to a...

The resultant force on the current loop $P Q R S$ due to a long current-carrying conductor will be, if the current flow in the loop is clockwise,
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(a) zero
(b) $0.36 \times 10^{-3} \mathrm{~N}$
(c) $1.8 \times 10^{-3} \mathrm{~N}$
(d) $0.5 \times 10^{-3} \mathrm{~N}$

Key Concepts

Magnetic Field Due to a Long Straight Conductor

A long straight conductor carrying a current produces a magnetic field that encircles it. According to the Biot–Savart law (or Ampere’s law for symmetric configurations), the magnitude of this magnetic field at a distance r from the wire is given by B = (?0 I)/(2?r). This concept is crucial because the strength of the magnetic field varies with distance, leading to different forces on parts of a nearby current loop.

Right-Hand Rule

The right-hand rule is a fundamental tool in electromagnetism used to determine the direction of magnetic forces on current-carrying conductors. When the thumb points in the direction of the current and the fingers in the direction of the magnetic field, the palm faces towards the direction of the force. This method is essential for understanding the direction of forces acting on different segments of a current loop in a magnetic field.

Magnetic Force on a Current-Carrying Conductor

This concept explains that a current-carrying conductor placed in a magnetic field experiences a force given by F = I (L × B), where I is the current, L is the length vector of the conductor, and B is the magnetic field. The magnitude and direction of this force are dependent on the orientation of the conductor relative to the magnetic field, and determining the net force on a complex current path often requires analyzing all individual segments of the conductor.

Interaction of a Current Loop with a Non-Uniform Magnetic Field

In cases where a current loop is placed in a non-uniform magnetic field, different segments of the loop can experience forces of varying magnitudes and directions. When parts of the loop are closer to a source of magnetic field (such as a long wire), the magnetic field strength is higher compared to the far side. This difference leads to a net force on the loop even if the overall current path forms a closed circuit. Analyzing these differences helps determine whether the net force is zero or non-zero.

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