Magnetic flux density or magnetic induction

Magnetic flux density is the amount or quantity of magnetic flux per unit area of a section that is perpendicular to the direction of flux. It may also be termed as magnetic induction. In simple language, it may be assumed to be the density of the magnetic field lines. The closer the lines, higher is the magnetic flux density.   
Magnetic flux density also equals the product of magnetic field strength and the magnetic permeability in the region in which the field exists. When electric charges pass through a magnetic field, they are subject to a force described by the equation F = qv x Bw, here
q is the amount of electric charge
x is the vector product
B v is the velocity of the charge
is the magnetic flux density at the position of the charge
The magnetic lines of force passing through unit normal area in a magnetic field is defined as magnetic induction.

How do we calculate the magnetic flux density?

The magnetic flux density is also called "B field" or "magnetic induction". The B field of magnets can be calculated with the help of understated formulae on the axis north-south-pole. The SI unit for magnetic flux density is the tesla which is equivalent to webers per square meter. This density is calculated by obtaining the number of webers per square metre; weber is the SI unit of magnetic flux. The overall flux density, however, is represented by the letter B.Mathematically, it is written as B =Φ/A where
B is magnetic flux density in teslas (T),
Φ is magnetic flux in webers (Wb),
A is area in square meters (m2). 
Magnetic Flux
It is measured in tesla (SI unit) or gauss (10 000 gauss = 1 tesla).
A permanent magnet produces a B field in its core along with its external surroundings. A B field strength along with the direction can be assigned to each point within and outside the magnet. If a small compass needle is placed in the B field of a magnet, it gets turned towards the field direction the force is also proportional to the B field.  

Direction of magnetic Induction:

B = Φ / A when A = 1m2. then B = Φ
 
Magnetic Flux density

Magnetic induction is a vector quantity. The direction in the magnetic field in which if a current carrying conductor is placed then no force acts on it, is known as the direction of magnetic induction.

You may view this video explaining magnetic flux density Calculation of magnetic induction due to a bar magnet

Calculation of magnetic flux for a bar magnet varies with the various positions. The formulae for various positions are listed below:

  • In axial position B = 2KM / r3

  • In equatorial position B = KM / r3

Here K = m0 / 4p = 10–7 Weber / A.m

Magnetizing field or intensity of magnetic field H

(a)  The ratio of magnetic induction produced in vacuum (Bo) and magnetic permeability of vacuum is defined as magnetising field (H), i.e. H = B0 / μ0
(b) The intensity of magnetic field due to a pole of strength mp at a distance r from it is H = mp/ μr2
(c)  Due to a small magnet H = M/r3 √1+3 cos2 θ

Difference between magnetic flux and magnetic field strength

Magnetic field strength (H) is the amount of magnetizing force. As stated above, it is proportional to the length of the conductor and the total current passing through the conductor. Hence, magnetic intensity is thus a vector quantity whose magnitude is the strength of a magnetic field at a point in the direction of the magnetic field at that point. The magnetic flux density, denoted by B is also a function of the magnetizing force H.
On the other hand, magnetic flux is the measure of the magnetic field strength of a two dimensional surface, say one particular side of a magnet. In text, it is usually depicted as a cluster of vectors attached to a geometrically abstract surface. Each vector intersects a separate point on the surface.

Illustration: 1000 turns per meter are wound over a Rowland ring of ferromagnetic material. On passing a current of 2 ampere in the coil, a magnetic field of 10 Wb/m2 is produced in it. The magnetizing force generated in the material will be:

(A) 1.2 × 10–3 A/m                (B) 2.6 × 10–3 A/m

(C) 2.6 × 0–4 A/m                  (D) 2 × 103 A/m

Solution: We know the formula of magnetizing force.

Hence, using the formula we get,

H= Ni / 2pr = ni = 103 × 2 = 2 × 103 

Hence, answer is (D) 2 × 103 A/m

Illustration: In the above problem, the value of intensity of magnetization in A/m will be:

(A) 7.96 × 106                        (B) 7.96 × 10–6

 (C) 3.98 × 103                        (D) zero

Solution: (A) B = m0 (I + H)

I = B / m0 – H = 10/4p × 10–7 – 2 × 103 = 7.96 × 106 A/m

You may also attempt to find the relative permeability of the material in the above illustration.

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