An iron bar magnet having a coercivity of \(4000 \mathrm{~A} / \mathrm{m}\) is to be demagnetized. If the bar is inserted within a cylindrical wire coil \(0.15\) \(\mathrm{m}\) long and having 100 turns, what electric current is required to generate the necessary magnetic field?

Imagine the space surrounding a magnet where its influence is felt — that's what we call a magnetic field. This invisible force field is crucial for understanding phenomena such as why a compass needle always points north or how electric motors function. The strength and direction of a magnetic field can be represented by vectors, with lines of force emanating from the north pole of a magnet, curving around, and entering the south pole.

Every charged particle in motion creates a magnetic field around it. It's the basis for the electromagnetism that drives much of our technology, from generators to MRI machines. The magnetic field inside a solenoid, which is a coil of wire, can be precisely controlled by changing the electric current that runs through the coil. This precise control is vital in many applications, including the demagnetization process described in the exercise above.

Ever tried sticking a magnet to your fridge and noticed it doesn't want to let go? That's coercivity in action! Coercivity measures a material's resistance to becoming demagnetized. It's an intrinsic property of ferromagnetic materials, like iron, that tells us how strong an external magnetic field must be to reduce the magnetization of the material to zero after it has been magnetized. This attribute is particularly important when we want to erase or write data on magnetic storage media or, as in our exercise, when demagnetizing a magnet.

In the demagnetization process, to effectively remove all magnetization, we apply an alternating magnetic field that gradually decreases in amplitude. This field has to exceed the coercive force at the beginning. The magnetic domains within the material, which were aligned to create magnetism, are randomly oriented during the process, eliminating the material's overall magnetic field.

Let's talk about solenoids: they are essentially coils of wire that can make you think of springs. When electric current passes through a solenoid, it generates a uniform magnetic field inside it, similar to a bar magnet, but with a crucial advantage: by varying the current, we can control the strength and polarity of this magnetic field. This makes solenoids extremely useful in science and technology for things like magnetic resonance imaging (MRI) and controlling valves or switches.

In our textbook example, the solenoid is used to create a magnetic field strong enough to demagnetize an iron bar. The number of turns of wire and the current passing through the coil govern how strong this magnetic field can get. So, understanding how a solenoid works is key to solving problems involving the creation of magnetic fields for various purposes, including the demagnetization process.