Dimensional Formula of Magnetic Field

A dimensional formula is a mathematical formula that represents a physical quantity in terms of fundamental quantities, such as mass, length, and time. By using dimensional formulae, we can see how fundamental quantities are raised to different powers to build a new physical quantity. The powers of fundamental physical quantities are referred to as dimensions.

What is a Magnetic Field? 

A magnetic field leads to the affection of other nearby magnetic materials, causing a force on them. The area near the magnet where the impact is experienced by the other magnet is termed a magnetic field. The magnetic field is the vector quantity that possesses both magnitude and direction. All the electrons have a property of angular momentum called spin. Most of the electrons form a pair in which one of the electrons spin up and the other spin down. In this case, the electron spins are opposite to each other which cancel out each other’s effect.

However, there are some atoms that consist of unpaired electrons which result in the creation of magnetic fields. The direction of the magnetic field is determined by the direction of the spin of the electron. It is denoted by B. For magnetic fields, the SI unit is Tesla.

Properties of Magnetic Field Lines:

1. Magnetic field lines do not cut across each other (if they do cut across each other, then at the point of intersection, there will be two directions which is not possible).
2. Around the magnet, magnetic field lines form a close loop. 
3. The direction of the magnetic field lines is fixed.
4. More density of the magnetic field lines indicates more strength of the magnetic field.

The force on a moving charged particle in a uniform magnetic field:

If a charged particle with a charge q moving with a velocity v enters into a magnetic field B, then it will experience a force which is given by 

F =q( v B )

On solving this, the magnitude of the force is given by:

F = qvB

The value of the force will be maximum when the angle between the velocity and magnetic field will be 90o.

So the maximum value of force is given by 

F = qvB

Here  (90o = 1)

The direction of this force will be normal to both the velocity and magnetic field. 

Dimensional Formula of a Magnetic Field

Since we found out the meaning of a magnetic field, let’s move on to its dimensional formula now. For any quantity, the dimensional formula is the expression showing the exponents to which the fundamental units can be raised to receive the single unit of the derived quantity. 

As we know, the force on a charged particle that is moving in the magnetic field is given by

 F = qvB …(1)

From equation (1) we get 

B = Fqv …(2)

The dimension of the force (F) is equal to [MLT-2].

The dimension of velocity (v) is equal to [LT-1].

The dimension of the charge (q) is equal to [AT].

Using the above values in the equation (2), we get,

B=MLT-2[LT-1][AT] 

On solving this, we get 

[M1L0T-2A-1]

where,

M = Mass

L = Length

T = Time

A = Ampere (current)

Magnetic Flux

The strength or the magnitude of the magnetic field is more in the vicinity of the poles (end of the magnet). Magnetic flux can be defined as the count of the magnetic field lines passing through a given cross-sectional area. It is denoted by . Mathematically, it is calculated by the dot product of a uniform magnetic field B and cross-sectional area A. For magnetic flux, the SI unit is weber (Wb). 

The amount of the magnetic flux is given by

= B . S

= BS

Where

B is the magnetic field.

S is the area vector.

is the angle in the middle of the magnetic field and the area.

For magnetic flux to be maximum, =00

= BS

For magnetic flux to be zero, =900

Applications of the Magnetism

1. Mass spectrometry 
2. Cathode Ray Tube (CRT)
3. Magnetic Resonance Imaging (MRI)
4. MagnetoCardiogram (MCG)

Electromagnetic Induction

Electromagnetic induction is a phenomenon of inducing a current in a coil by moving the coil back and forth within a magnetic field of a stationary bar magnet. This law was discovered by Michael Faraday. The principle of electromagnetic induction is used in motors, generators and transformers. This law created a way to produce electricity in a circuit without using the battery and through the force of magnetic fields.

Conclusion

Magnetic field is the quantity that is associated with each and every point in the space where the magnet is present. A line drawn tangent to the magnetic field represents its direction. The magnetic field can be considered similar to the gravitational field, as both of them involve action-at-a-distance force. It plays a significant role in many areas of physics. When the magnetic field lines and electric field lines combine, they result in the formation of electromagnetic fields.