Animated Solution for Physics - Magnetic Effects of Current: The coercivity of a small magnet where the ferromagnet gets demagnetised is $3\times 10^3{\text{ Am}}^{-1}$. The current required to be passed in a solenoid of length $10\text{ cm}$ and number of turns $100$, so that the magnet gets demagnetised when inside the solenoid is

Imagine a small ferromagnetic material that has been magnetized. It has a "memory" of the magnetic field it was exposed to. To wipe this magnetic memory and completely demagnetize it, we must apply a reverse magnetic field. The exact intensity of this reverse field required to bring the material's net magnetization back to zero is called its coercivity.

In this problem, we are given a small magnet with a coercivity of $H=3\times 10^3\text{ A/m}$. To generate this reverse field, we place the magnet inside a solenoid and pass a current through it.

Magnetic Intensity vs. Magnetic Field

A very common pitfall here is confusing Magnetic Field ($B$) with Magnetic Intensity ($H$).

Students often rush to use the formula $B={\mu }_{0}nI$. However, look closely at the units of coercivity given in the problem: $\text{A/m}$. This is the SI unit for Magnetic Intensity ($H$), not Magnetic Field ($B$, which is measured in Tesla).

The relationship between them in a vacuum (or air core) is $B={\mu }_{0}H$. Therefore, the formula for the magnetic intensity inside a long solenoid is simply:

where $n$ is the number of turns per unit length, and $I$ is the current.

We are given the total number of turns $N=100$ and the length of the solenoid $l=10\text{ cm}$.

Before we plug anything in, we must ensure all our units are in the standard SI system. The length must be converted to meters:

Now, we can calculate the turns density, $n$:

Now we substitute our known values into the magnetic intensity equation. We know the required coercivity $H$ is $3\times 10^3\text{ A/m}$, and our turns density $n$ is $1000{\text{ m}}^{-1}$.

Dividing both sides by $1000$, we find the required current:

This means a current of $3\text{ A}$ is exactly what is needed to generate a strong enough reverse field to completely demagnetize our small ferromagnet.

Food for thought: If we were dealing with a material meant to be a permanent magnet (like Alnico or steel), its coercivity would be much higher, requiring a significantly larger current to demagnetize it. This is why permanent magnets are "permanent"—they resist losing their magnetization!