A closed Loop PQRS carrying a current is placed in a uniform...

A closed Loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segment $\mathrm{PS}, \mathrm{SR}$ and $\mathrm{RQ}$ are $\mathrm{F}_{1}, \mathrm{~F}_{2}$ and $\mathrm{F}_{3}$ respectively and are in the plane of the paper and along the directions shown, the force on the segment $\mathrm{QP}$ is(b) $\mathrm{F}_{1}-\mathrm{F}_{2}+\mathrm{F}_{3}$ (c) $-\mathrm{F}_{1}+\mathrm{F}_{2}+\mathrm{F}_{3}$

A closed Loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segment $\mathrm{PS}, \mathrm{SR}$ and $\mathrm{RQ}$ are $\mathrm{F}_{1}, \mathrm{~F}_{2}$ and $\mathrm{F}_{3}$ respectively and are in the plane of the paper and along the directions shown, the force on the segment $\mathrm{QP}$ is(b) $\mathrm{F}_{1}-\mathrm{F}_{2}+\mathrm{F}_{3}$
(c) $-\mathrm{F}_{1}+\mathrm{F}_{2}+\mathrm{F}_{3}$

Key Concepts

Uniform Magnetic Field

A uniform magnetic field is one in which the magnetic field strength and direction remain constant throughout the region of interest. In problems involving current-carrying conductors placed in such a field, each segment of the conductor experiences a magnetic force of predictable magnitude and direction based on its orientation and current direction.

Closed Current Loop and Equilibrium

In a closed loop, the conductor forms a continuous circuit, and the magnetic forces acting on different segments of the loop must combine to give a net force. In many cases, particularly in a uniform magnetic field, the overall net force on the loop is zero due to symmetry or by virtue of Kirchhoff's laws, even though individual segments may experience non-zero forces.

Magnetic Force on a Current-Carrying Conductor

This concept explains that when a conductor carrying an electrical current is placed in a magnetic field, it experiences a force described by the vector equation F = I (L × B), where I is the current, L is the length vector of the conductor, and B is the magnetic field. The direction of the force is determined by the cross product of L and B, meaning it is perpendicular to both the direction of the current and the magnetic field.

Superposition of Forces

This principle involves the vector addition of multiple forces acting on different segments of the conductor. In the context of a closed current loop in a magnetic field, the forces on each segment add up such that the force on one segment can be expressed as the negative sum of the forces on the other segments, ensuring that the total force on the complete loop sums to zero.

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