Question

prove that electric field vector, magnetic field vector and direction of propagation are mutually perpendicular to each other

Answer 1

Answer:

Consider Maxwell's equation.

Explanation:

∇ × B = ( 1/ c) ∂E/ ∂t .

where B is the vector of the magnetic field and E is the vector of the electric field

The partial derivative of E with respect to time is a vector pointing in the same direction as E. The left side is a cross product that produces a vector perpendicular to B.

therefore E will be perpendicular to B.

In a monochromatic electromagnetic plane wave of angular frequency w propagating in a vacuum, for example, the vector of complex constant amplitude of the plane wave E and B of the electric field E(r,t) and magnetic field B(r,t) verify

wB = k × E

where

k is the "wave vector," also known as the "propagation vector," because it contains the direction of the wave's propagation, which is also the direction of the electromagnetic wave's energy flow (Of course, "" is the vector product of two vectors).

This relationship clearly shows that E and B are perpendicular to each other, as are E(r,t) and B(r,t), and that B(r,t) is perpendicular to (k) the direction of propagation.

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