The magnetic field existing in a region is given by B⃗=B0[1+(x)/(l)] A square loop of edge l and

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The magnetic field existing in a region is given by...

The magnetic field existing in a region is given by $\vec{B}=B_{0}\left[1+\frac{x}{l}\right]$ A square loop of edge $l$ and carrying current $I$ is placed with its edges parallel to the $x-y$ axis. The magnitude of the net magnetic force experienced by the loop is : (a) $2 B_{0} n$ (b) $B_{0} I_{0} l$ (c) $B_{0} I l$ (d) $B I l$

The magnetic field existing in a region is given by $\vec{B}=B_{0}\left[1+\frac{x}{l}\right]$
A square loop of edge $l$ and carrying current $I$ is placed with its edges parallel to the $x-y$ axis. The magnitude of the net magnetic force experienced by the loop is :
(a) $2 B_{0} n$
(b) $B_{0} I_{0} l$
(c) $B_{0} I l$
(d) $B I l$

Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept explains that when a conductor carrying an electric current is placed in a magnetic field, it experiences a force given by the cross product of the current element and the magnetic field. This fundamental idea is captured by the expression F = I (L × B), where I is the current, L is the length vector of the conductor, and B is the magnetic field.

Non-uniform Magnetic Field

A non-uniform magnetic field is one that varies with position. This spatial variation means that different parts of a conductor or current loop experience different magnetic field strengths, leading to unbalanced forces. Understanding this is crucial when evaluating the net force on systems like loops, where a uniform field would yield canceling forces.

Closed Current Loop Force Analysis

In a closed current loop, forces on different segments can cancel out when the magnetic field is uniform. However, in a non-uniform magnetic field, because the field strength changes along the loop, the forces do not exactly cancel, resulting in a net force. Analyzing each segment's contribution is essential to correctly determine the overall force acting on the loop.

Magnetic Dipole in a Gradient Field

A current loop behaves like a magnetic dipole characterized by its magnetic moment. When placed in a magnetic field gradient, the dipole experiences a net force proportional to the gradient of the magnetic field. This concept connects the properties of the loop with the spatial behavior of the magnetic field, explaining why non-uniformity leads to a net force on the loop.

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