Dimensions of Magnetic Field

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Basics Of Dimensional Formula

A physical quantity is any quantity that can be measured with a device in terms of units. The entire list of physical quantities can be broadly classified into two types namely fundamental physical quantities and derived physical quantities. 

The subsequent sections of this page give a brief description of the basic idea of physical quantities and the dimensional formula for the magnetic field. The page also provides a glimpse of different units of measurement. 

Dimensional Formula of Magnetic Field = M1 T2 I -1


Physical Quantities

All physical quantities can be broadly classified into two types namely fundamental or base physical quantities and derived physical quantities. There are seven fundamental physical quantities in Physics. They are Mass, time, length, electric current, temperature, luminous intensity, and amount of substance. These seven quantities are called the dimensions of the physical world. Instead of using the names, their first letters are used to represent the base quantities. The three mechanical quantities: mass, length and time are represented as M, L and T. In order to represent the dimensions, these symbols are used within a pair of square brackets. 

It is important to note that the dimensions of a physical quantity and the dimensions of their unit are the same. It is only the nature of the unit represented as [M], [L] and [T], and not its magnitude. Every derived physical quantity is represented in terms of its fundamental physical quantities with appropriate power. The powers to which the fundamental physical quantity should be raised to obtain the derived quantity is called the dimensions of the derived quantity.


More about Dimensional Formula and Dimensional Equation

The dimensional formula is a complex expression that narrates which fundamental quantities are involved and how are they involved in modelling the derived physical quantity. The physical quantity and its dimensions are equated in an equation called the dimensional equation. In other words, dimensional equations are the equations that represent the dimensions of any physical quantity in terms of its fundamental quantities.


Magnetic Field

The region around the magnet, where there is an influence of the force by that magnet, is called the Magnetic field. Magnetic fields can be created by moving electric charges. The magnetic field penetrates through space and acts as a driving force to move electric charges and magnetic dipoles. 

In case of a bar magnet, the magnetic field lines are stronger at the poles and weaker at the middle of the bar magnet. The strength of the magnetic field at both poles is the same. A magnetic field is a derived physical quantity. The dimensional formula of a magnetic field is equal to [M]1 [T]-2 [I]-1


Dimensional Formula of Magnetic Field

The dimensional formula of a magnetic field can be defined as the representation of units of a magnetic field in terms of fundamental physical quantities with appropriate power. The dimensional formula of Magnetic field is given as [M]1 [T]-2 [I]-1. In this formula, ‘M’ represents the mass, ‘T’ represents the time, and ‘I’ represents the current.


Derivation of Dimensional Formula Of Magnetic Field

The Lorentz force is given by the equation,

Force = Charge x Magnetic Field (B) x Velocity

The above equation can be rewritten to find the magnetic field as:

Magnetic field = Force x [Charge x Velocity]-1 → (1)

We know that the velocity can be written in terms of distance and time as:

Velocity = Distance x [Time]-1

The dimensional formula of velocity is [L T-1] → (2)

The basic formula for electric charge is 

Charge = Electric Current x time

The dimensional formula for electric charge is [I1 T1] → (3)

The Lorentz force is given by Newton’s second law of motion as:

Lorentz force = Mass x Acceleration → (4)

But acceleration is the rate of change of velocity and is given as:

Acceleration = Velocity x [Time]-1 → (5)

Substituting (5) in (4), we get

Lorentz force = Mass x Velocity x [Time]-1

The dimensional formula for Lorentz force is thus written as [M L T-2] → (6)

Substituting the dimensions of velocity, electric charge, and Lorentz force from (2), (3) and (6) in the formula for Magnetic field represented as (1), we get,

Therefore B = [M L T-2] {[I1 T1] [L T-1]}-1

B = [M1 L0 T-2 I-1]

Therefore, the magnetic field can be dimensionally represented as [M1 T2 I-1].

FAQ (Frequently Asked Questions)

1. What are the limitations of Dimensional Analysis?

Ans: Though dimensional analysis has an ample of applications, it has a list of limitations too. The limitations of dimensional analysis are:

  • This is not valid for proportionality constants and dimensionless quantities. 

  • Dimensional analysis is not valid for trigonometric, logarithmic, and exponential functions. 

  • This method of analysis is complicated in case of physical quantities which are dependent on more than three physical quantities. 

  • In cases where the constant of proportionality has dimensions, this method of analysis cannot be used. 

  • The equations that contain addition or subtraction of two quantities cannot be derived.

2. What are the advantages of the Dimensional formula?

Ans: Dimensional formulas can be used to convert units of any physical quantity from one system of units to another system of units. These formulas are also employed in deriving relations between various physical quantities on the basis of their interdependence. The formulas also explain how the physical quantities can be expressed in terms of their fundamental units. It can also be used to check the correctness of a given equation.