Animated Solution for Physics - Magnetic Effects of Current: A bar magnet is demagnetised by inserting it inside a solenoid of length $0.2\text{ m}$, $100$ turns and carrying a current of $5.2\text{ A}$. The coercivity of the bar magnet is

Imagine you have a powerful bar magnet. It has a 'memory' of its magnetic state, holding onto its North and South poles stubbornly. But what if we want to wipe that memory clean? What if we want to completely demagnetise it? This is where the concept of coercivity comes into play.

Coercivity is defined as the exact amount of reverse magnetic field intensity, denoted by $H$, required to reduce the residual magnetisation of a material to absolute zero. Think of it as the opposing force needed to perfectly cancel out the magnet's internal alignment.

To achieve this in a controlled manner, we place the bar magnet inside a solenoid. A solenoid is essentially a long coil of wire. When we pass an electric current through it, it generates a highly uniform magnetic field along its central axis. By orienting the magnet such that its field opposes the solenoid's field, we can carefully dial up the current until the magnet is wiped clean.

The beauty of the magnetic field intensity $H$ inside a long solenoid is that it depends purely on the geometry of the coil and the current flowing through it. It is completely independent of the core material. The formula is elegantly simple:

Here, $n$ represents the number of turns per unit length of the solenoid, and $I$ is the current. We can expand $n$ as the total number of turns $N$ divided by the total length $l$:

Now, let's bring in the numbers from our specific problem. We are given a solenoid with a total of $N=100$ turns, a length of $l=0.2\text{ m}$, and a current of $I=5.2\text{ A}$. Let's substitute these values into our master equation:

First, let's find the turn density $n$. Dividing $100$ by $0.2$ gives us $500$ turns per meter. This means for every meter of this solenoid, there are $500$ loops of wire tightly packed together.

Finally, multiplying $500$ by $5.2$ gives us the total magnetic field intensity:

Our final answer is $2600\text{ A/m}$. This is the coercivity of the bar magnet.

Why does this matter in the real world? If you are engineering a permanent magnet for an electric motor or a hard drive, you want a material with a very high coercivity. You want it to be stubborn so that stray magnetic fields don't accidentally erase its data or weaken the motor. Conversely, for transformer cores, you want materials with very low coercivity so they can switch magnetic states rapidly without wasting energy.