Animated Solution for Physics - Magnetic Effects of Current: If a current is passed through a spring, then the spring will

A Spring in a Circuit

Imagine a simple electrical circuit where a metallic spring is connected in series with a DC voltage source. When the switch is closed, a steady current $I$ begins to flow through the entire length of the spring.

At first glance, it might seem like nothing special should happen. After all, it's just a wire carrying current. However, the coiled geometry of the spring introduces a fascinating electromagnetic effect.

Adjacent Turns as Parallel Wires

To understand the physics at play, we need to look closely at the individual turns (or coils) of the spring. Because the spring is a continuous piece of wire wound into a helix, the current flows sequentially from one turn to the next.

If we isolate any two adjacent turns, they effectively act like two parallel conducting wires placed very close to each other. More importantly, because the current is flowing continuously down the helix, the direction of the current in these two adjacent turns is exactly the same.

This is where the magic of electromagnetism comes in. According to Ampere's Force Law, when two parallel wires carry current, they exert a magnetic force on each other. The magnitude of this force per unit length is given by:

The crucial part of this law is the direction of the force: If the currents flow in opposite directions, the wires repel each other. If the currents flow in the same direction, the wires attract each other.

Since the current in our adjacent spring turns is flowing in the same direction, they experience an attractive magnetic force.

Compression

Now, apply this logic to the entire spring. Every single turn is magnetically attracting the turn directly above it and the turn directly below it. This creates a net inward pull across the entire length of the spring.

As a result of this collective attractive force, the spring compresses.

What about AC?

What would happen if we replaced the DC battery with an Alternating Current (AC) source? The current would constantly reverse its direction.

However, even though the current reverses, it reverses everywhere in the circuit simultaneously. This means that at any given instant, the current in adjacent turns is still flowing in the same direction. Therefore, the magnetic force between the turns remains attractive at all times. The spring will still compress, but because the magnitude of the current is oscillating, the spring will vibrate (oscillate) at twice the frequency of the AC source!