Page 25 - Electrostatics-11

© GC Shiba

Principle of homogeneity (same origin)

For any given correct equation, the dimension of left-hand side is equal with the

dimension of right-hand side. This is called principle of homogeneity.

For e.g., A = B + C

Here, quantity A represents the sum of B and C. So, dimension of A must

be equals with dimension of B + C. Furthermore, quantity B and C are added

here. So, we can conclude that both represents the same physical quantity

because only similar quantity can be added or subtracted.

∴ = +

Four categories of physical quantities

• Dimensionless variables: Physical quantities having neither dimension nor

constant values are called dimensionless variables. E.g., specific gravity

(relative density), mechanical advantage, velocity ratio, refractive index etc.

• Dimensionless constant: Physical quantities having neither dimension nor

different values are called dimensionless constant. E.g., (pi), numerical

(counting) numbers etc.

• Dimensional variables: Physical quantities having dimension with

different values. E.g., length, mass, acceleration, velocity, amount of

substance etc.

• Dimensional constant: Physical quantities having dimension along with

constant values. E.g., gravitational constant, velocity of light, light year etc.

2 Mechanics