# Magnetic Field Intensity

## What is Magnetic Field Intensity?

The force of attraction or repulsion experienced by an unit north pole strength placed in the magnetic field of a magnet is called the magnetic field intensity.

### Magnetic Field

Magnetic field is defined as the space around a magnet in which its influence of magnetic force of attraction or repulsion is experienced by small magnets.

Magnetic field intensity is also known as strength of a magnetic field. It is denoted by ( B ) .

Let, ( q_m ) is the pole strength of a magnet. Then by Coulomb’s law of magnetic forces, the force experienced by the unit North pole will be –

F = \frac {\mu_0}{4 \pi} \left ( \frac {q_{m} \times 1}{r^2} \right )

= \left ( \frac {\mu_0}{4 \pi r^2} \right ) q_{m}

Since, at a point at distance ( r ) in the field, the term \left ( \frac {\mu_0}{4 \pi r^2} \right ) becomes a constant. Hence, it can be replaced by another term ( B ) which is called intensity or strength of magnetic field.

Therefore, \quad F = B \times q_{m}

Or, \quad B = \left ( \frac {F}{q_{m}} \right )

= \frac {\text {Magnetic force on unit North pole}}{\text {Pole strength}}

Thus, strength or intensity of magnetic field at a point is defined as the ratio of force acting on an imaginary unit north pole placed at that point to the pole strength of the magnet.

## Field Lines

Field lines are imaginary curved lines representing the magnetic field of a magnet.

The tangent at any point of field lines gives the direction of magnetic field at that point.

Field of a magnet may be of two types –

1. Uniform magnetic field.
2. Non-uniform magnetic field.

### Uniform Magnetic Field

If magnetic field has same strength and same direction at all points in the its region, then it is called a uniform magnetic field.

Uniform magnetic field lines are represented by equidistant set of parallel field lines. Figures (A), (B) and (C) represent uniform magnetic field lines in different directions.

1. Figure (A) represents uniform magnetic field lines which are parallel to the plane of paper.
2. Figure (B) represents uniform magnetic field lines which are perpendicular to the plane of figure. These are in inward direction i.e., penetrating into the plane of figure.
3. Figure (C) represents uniform magnetic field lines which are perpendicular to the plane of figure. These are in outward direction i.e., emerging out from under the plane of figure.

### Non-uniform Magnetic Field

If magnetic field has different strength at different points in the field region, it is called a non-uniform magnetic field as shown in figure (D).

In a non-uniform magnetic field, the magnitude and direction of magnetic field vary at different points in the field region. It is represented by converging, diverging or unequally spaced field lines.

## Properties of Field Lines

Field lines of a magnet have the following properties :

1. Field lines are continuous and closed curves travelling from North pole to South pole at outside the magnet body and from South pole to North pole inside the magnet body.
2. The tangent at any point on the field line gives the direction of intensity of field ( B ) at that point.
3. Two field lines do not intersect or cross to each other.
4. Widely spaced field lines represent weak field and closely spaced field lines represent strong field.
5. Magnetic field lines are imaginary but they represent full aspect of a magnetic field which is a real phenomenon.

## Difference between Electric & Magnetic Field Lines

 Electric Field Lines Magnetic Field Lines These are generally discontinuous. These are continuous and closed curves. These imaginary lines not exist within the charged conductor. These imaginary lines exist within the body of magnet. Electric field lines do not exist within the charged conductor, the electric field inside the charged conductor is zero. Magnetic field lines exist inside the material and magnetic field is never zero inside a magnet body.

## Magnetic Flux

Magnetic flux is defined as the number of field lines passing through a given surface. It is denoted by ( \phi ) .

SI unit of magnetic flux is weber ( Wb ) .

### Magnetic Flux density

The number of field lines passing normally through unit area of a surface is called as magnetic flux density. It is denoted by ( B ) .

If ( \phi ) is the number of flux passing normally through a surface of area ( A ) , then magnetic flux density is given by –

B = \left ( \frac {\phi}{A} \right )

Magnetic flux density is a vector quantity.

In SI system its unit is tesla ( T ) \ \text {or ( Wb-m}^2 )

In CGS system its unit is gauss ( G )

1 G = 10^{-4} T