Concept of Magnetic field:

A magnetic field is defined as a tool that describes the way by which the magnetic forces gets distributed in the space around and also within something magnetic. There are several ways by which magnetic fields can be described. Mathematically magnetic fields can be described as vector field. This vector field can be plotted directly as a set of many vectors that are drawn on a grid. Each vector points in the direction that a compass would point have length dependent on the strength of the magnetic force. While arranging for many small compasses in a grid pattern and placing the grid in a magnetic field helps in illustrating the technique of magnetic field. The only difference in this case is that it does not indicate the strength of the magnetic field. An alternative way to describe the magnetic field is by representing the information that are contained within a vector field while using the field lines. Here the grid lines are dispensed and connected to the vectors with smooth lines. The characteristics of field lines include as follows-

1. Magnetic field lines never cross.

2. Magnetic field lines naturally bunch together in regions where the magnetic field is the strongest. This means that the density of field lines indicates the strength of the field.

3. Magnetic field lines don't start or stop anywhere, they always make closed loops and will continue inside a magnetic material.

4. In order to indicate the direction of the field lines, arrowheads are generally drawn along with the lines. Sometimes these arrowheads are not drawn and the directions are indicated in a different way. One of the region is labeled as north and the other is labeled south and field lines are drawn from the poles. The field is assumed to follow the lines from the north to south. The labels of N and S are usually placed at the ends of the magnetic field source which stand out to be strictly arbitrary and there exists nothing special about these type of locations.

5. Field lines can be visualized quite easily in the real world. This is commonly done with iron filings dropped on a surface near something magnetic. Each filing behaves like a tiny magnet with a north and South Pole. The filings naturally separate from each other because similar poles repel each other. The result is a pattern that resembles field lines. While the general pattern will always be the same, the exact position and density of lines of filings depends on how the filings happened to fall, their size and magnetic properties.

Detection of magnetic field with the help of compass:

Any source of magnetism, such as a magnet or electromagnet, is surrounded by a magnetic field. That field can be detected by various devices, which can also give information about the direction of the field and even its strength.

As magnetic field is a type of vector quantity, there are two types of aspects that needs to be measured in terms of strength and direction. The way to measure direction is quite easy.  In this case a magnetic compass is used which lines up with the field. The magnetic compasses ae used for the purpose of the navigation using the magnetic field of the Earth. A compass is simply a thin magnet or magnetized iron needle balanced on a pivot. It can be used to detect small magnetic fields. The needle will rotate to point toward the opposite pole of a magnet. It can be very sensitive to small magnetic fields. The compass was used to discover that the Earth is a huge magnet. The North-seeking pole of the compass needle will always point toward the Earth's North magnetic pole.

However measuring the strength of the magnetic field is a quite difficult one. Practical magnetometers are used in this case which came in the 19^th century. Most of these magnetometers work by exploiting the force an electron feels as it moves through a magnetic field. Very accurate measurement of small magnetic fields has only been practical since the discovery in 1988 of giant magneto resistance in specially layered materials. This discovery in fundamental physics was quickly applied to the magnetic hard-disk technology used for storing data in computers. This led to a thousand of increase in the data storage capacity in just a few years after following the implementation of the technology. Magnetic field is measured in tesla in SI system. The Tesla is defined as the amount of force that is applied to a moving charge due to the field.

Gauss meters are used to measure the strength of a magnetic field. They use a electronic chip called a Hall effect device, which gives off a tiny electrical current when exposed to a magnetic field. The current is amplified with electronic circuitry and a meter shows the number of gauss 

Magnetic fields occur whenever charge is in motion. As more charge is put in more motion, the strength of a magnetic field increases. Magnetism and magnetic fields are one aspect of the electromagnetic force, one of the four fundamental forces of nature.

There are two basic ways which we can arrange for charge to be in motion and generate a useful magnetic field:

1. We make a current flow through a wire, for example by connecting it to a battery. As we increase the current (amount of charge in motion) the field increases proportionally. As we move further away from the wire, the field we see drops off proportionally with the distance. This is described by Ampere's law. Simplified to tell us the magnetic field at a distance rrr from a long straight wire carrying current I the equation becomes-

B= μ0​I / 2πr

Here μ0 is a special constant known as the permeability of free space.

Since the magnetic field is a vector, we also need to know the direction. For conventional current flowing through a straight wire this can be found by the right-hand-grip-rule.