## What is a magnetic field?

A magnet is a material around which there always exists a magnetic field. These materials are also known as lodestones. They were named magnets on a Greek province named Magnesia. There are various types of magnets. One of them is a bar magnet. A bar magnet has two poles or ends, namely the north pole and the south pole. If we bring the north pole close to the north pole of another magnet, then they repel each other. Unlike poles like north and south attract one another. There must be a force that is helping the magnets attract or repel. This force is a magnetic field around the magnet. As a hard-and-fast rule, magnetic field lines always travel from the north pole to the south pole.

## Magnetic permeability

It is the ability of a material to let magnetic force pass through it and is represented by μ. To evaluate this we use relative permeability (μr) which is the ratio of magnetic permeability of the material (μ) to the magnetic permeability of free space (μ0).

### ${\mu }_{r}=\frac{\mu }{{\mu }_{0}}$

where

μ0= 4Π x 10-7 Wb A-1 m-1

The relative permeability of air or aluminum is 1, while for iron it is 5000. This means that with a higher value of relative permeability, the material will be magnetized more easily.

## Electromagnetism

A straight wire, carrying current makes a magnetic field around it. This field can be strengthened if the wire is curved, making two segments. The magnetic field produced by two segments makes a denser and stronger field. The helical shape of a coil allows the creation of multiple segments. If we put a ferromagnetic material like iron inside the coil, then it will gain temporary magnetism. We know this setup as an electromagnet. The negative charge carriers are electrons and the positive charge carriers are protons. While, in electricity, negative charge or positive charge can be isolated, this is not the case with magnets. It is impossible to divide a magnet into a monopole magnet. Every time a magnet is divided, it leads to two poles- north and south.

As we know that the AC signal oscillates between positive and negative cycles, the magnetic field generated by this will also oscillate. If we connect a conductor to an AC source, the conductor will produce electromagnetic waves. These electromagnetic waves can travel through a medium. One of many applications of these is radio frequencies. When a frequency is created at the emitter end, it produces electromagnetic waves that travel to the transmitter end.

### Magnetostatics

The study of a magnetic field around a conductor carrying a current which does not change with time is known as magnetostatics. It is similar to electrostatics where the charges are stationary. This theory has its applications in computer storage devices.

### Solenoid

A solenoid is one application of electromagnetism. It is a wire coil wound on a rod-shaped object preferably made of a ferromagnetic material. A solenoid converts the electrical energy to the magnetic field and this magnetic field is used to achieve linear motion of the rod-shaped object inside the coil. This is a temporary magnet because it gets magnetized only when current is passed through the helical coil; otherwise, it loses its magnetism.

### Superconducting magnet

A superconductor is a material that offers zero resistance to the flow of current. An electromagnet created by using coils made of superconducting material is a superconducting magnet. These devices can produce greater magnetic fields than most non-superconducting magnets and can bring down the operating cost. These types of magnets are often used in MRI machines, fusion reactors, and particle accelerators.

## Right-hand rules

If a conductor is carrying a current, then it possesses a magnetic field around it. The question is, how do we find the direction of the magnetic field? For this purpose, we take an example of a current-carrying straight wire. If we grab the straight wire with our right hand and put the thumb finger toward the electric current, the remaining fingers will point towards the direction of the magnetic force. So if the current is flowing upwards in the wire, the top view will show us that the direction of the magnetic force is in an anti-clockwise direction. This is the first right-hand rule and was first shown by Oersted.

## Lorentz force

The direction of the force of the magnetic field on the current passing through a conductor is perpendicular to both the magnetic field and the current. Lorentz force is the combined effect of an electric and a magnetic force on a point charge because of the electromagnetic field.

According to the second right-hand rule, if the thumb represents the direction of an electric current, the index finger represents the direction of a magnetic field, then the direction of the force acting on the charged particle is determined by the middle finger. In the figure below, B, I, and F are perpendicular to each other in a three-dimensional plane.

The relation between the magnetic force on the current-carrying conductor is given by

$\stackrel{⇀}{F}=q\left(\stackrel{⇀}{E}+\stackrel{⇀}{v}B\mathrm{sin}\theta \right)$

where

F is the magnetic force on the current-carrying conductor.

q is the value of the charge.

E is the external electric field.

v is the velocity of the charge.

B is a magnetic field, also known as B-field.

θ is the angle between the direction of magnetic force and current.

Magnetic force is maximum when θ is 90° or the magnetic force is perpendicular to the current

It is negligible when θ is 0° or when the magnetic force is parallel to the current. The product qvB is directly proportional to the magnetic force acting on the conductor.

The high current, which means the higher velocity of electrons will lead to stronger magnetism. When a charge moving in magnetic field experiences a force, then the force is always perpendicular to velocity and field. Any force that is perpendicular to velocity does not change the speed but it can change the charge direction.

## Right-hand rule for solenoid

In the case of the first right-hand rule, if we grab a solenoid instead of the straight wire then the thumb will point to the direction of the magnetic field induced by the solenoid.

## Ampere's circuital law

In 1826, scientist André-Marie Ampère stated that the line integral of magnetic field density in a closed path is equal to the product of the current in the closed path and the magnetic permeability of free space.

where

B is the magnetic field and its line integral with respect to length is done.

μ0 is the magnetic permeability of free space.

I is electric current through the closed path.

## Context and Applications

This concept holds relevance in diploma, undergraduate, and postgraduate degrees, which requires the fundamentals of college physics, such as

• Bachelors in Science in Physics
• Bachelors in Electrical Engineering
• Bachelors in Aerospace Engineering
• Masters in Material Science and Engineering

## Practice Problems

1. Which of the following is a permanent magnet?

1. Iron nails
2. Neodymium
3. Solenoid
4. Electromagnet

Explanation: Neodymium is the strongest permanent magnet. The rest of the options are temporary magnets.

2. What is the direction of the magnetic field in a magnet?

1. From north to south.
2. From south to north.
3. Direction is not fixed.
4. Depends on the magnet.

Explanation: The magnetic field lines travel from north to south conventionally, just as we have assumed that electric current travels from positive to the negative terminal.

3. Which of the following is not a superconductor?

1. Mercury
3. Aluminum
4. Iron

Explanation: Some examples of superconductors are pure metals, such as aluminum, lead, mercury. Iron is not a superconductor.

4. What is the SI unit of electric charge?

1. Ohm
2. Ampere
3. Coulomb
4. Tesla

Explanation: The SI unit of electric charge is Coulomb.

5. Permanent magnet Alnico is composed of which of the following elements?

1. Cobalt, Aluminum, and Nickel
2. Copper, Iron, and Magnesium
3. Zinc, Aluminum, and Silver
4. Chromium, Phosphate, and Uranium

Explanation: Alnico is an alloy made from Aluminum, Nickel, and Cobalt.

• Hyperphysics
• Gauss's law

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