Answer to Question #135398 in Mechanics | Relativity for Ada

Question

The intensity, I, of an electromagnetic wave is related to the electric field strength E and magnetic induction B of the fields producing it by the equation I = E.B / 20 where 0 is the permeability of free space. Show that this equation is homogeneous.

Answer 1

Given intensity of the wave is $I = \frac{EB}{2\mu_0}$

Equation is homogeneous if dimension of both sides are same.

Dimension of Intensity, I = $[ML^0T^{-3}]$

Dimension of Electric Field, E = $[MLT^{-3}A^{-1}]$

Dimension of magnetic field, B = $[ML^0T^{-2}A^{-1}]$

Dimension of $\mu_0$ = $[MLT^{-2}A^{-2}]$

Dimension of right hand side of the equation,

$\frac{[MLT^{-3}A^{-1}][ML^0T^{-2}A^{-1}]}{[MLT^{-2}A^{-2}]} = [ML^0T^{-3}]$

Since, both side dimensions are same, hence equation is homogeneous.