Animated Solution for Physics - Magnetic Effects of Current: A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

Now, imagine a uniform magnetic field $\mathbf{B}$ piercing straight down through the table, into the plane of the paper. Our goal is to determine how this magnetic field interacts with the current loop. Will it push the loop? Will it twist it? Or will it do something else entirely?

The magnetic force $d\mathbf{F}$ acting on an infinitesimally small current element $d\mathbf{l}$ is given by the fundamental cross-product relation:

This equation tells us that the force is always perpendicular to both the direction of the current and the magnetic field.

Point your forefinger in the direction of the magnetic field (into the page). Now, point your middle finger in the direction of the current at any point on the loop (tangential to the circle). You will notice that your thumb, which represents the force, points radially outward away from the center of the loop.

If you repeat this exercise for every single point around the circumference of the loop, you will find that every tiny segment of the wire experiences a force pulling it directly away from the center.

Internal Tension Because the loop is perfectly symmetric and the magnetic field is uniform, for every force vector pointing outward on one side, there is an equal and opposite force vector pointing outward on the exact opposite side. When we sum up all these forces, they perfectly cancel each other out:

A net force of zero means the center of mass of the loop will not accelerate; it will not translate towards the $+x$ or $-x$ axis.

However, just because the net force is zero doesn't mean the forces have no effect! Imagine a group of people standing in a circle, holding hands, and all leaning backward. The group as a whole doesn't move, but their arms are under immense tension. Similarly, the radially outward magnetic forces create tension within the wire, pulling it outward in all directions. Consequently, the loop will have a strong tendency to expand.