Electromagnetic waves and their features

Q: How the electromagnetic waves are produced?

Ans: We know that a charge at rest produces an electric field around it but no magnetic field where a moving charge produces both electric and magnetic fields but if the charge is moving with constant velocity there will be no charge in the values of the electric and magnetic fields,So all electromagnetic waves are produced.Now if charge is moving with non zero acceleration, both the electric and magnetic field will change, there by producing the em waves. So we conclude that an accelerated charge emits electromagnetic waves. Continue reading “Electromagnetic waves and their features”

More characteristics or properties of transverse electric and magnetic waves in parallel planes

Last time I have discussed the few characteristics or properties of transverse electric and magnetic waves in parallel planes. Let us discuss more properties of TE and TM waves like cut-off wavelength, guide wavelength, phase velocity, group velocity:

(a) Cut – off Wavelength

גc = υ0/fc

Put the value of υ0 and fc in above equation,

Or                        גc = 1/√ μ0ε0   2 α√ μ0ε0/m

                 גc = 2 α/m

The above is the expression for the cut-off wavelength. Continue reading “More characteristics or properties of transverse electric and magnetic waves in parallel planes”

CHARACTERISTICS OF TRANSVERSE ELECTRIC AND TRANSVERSE ELECTRIC WAVES

The characteristics or properties of transverse electric (TE) and transverse magnetic (TM) in parallel planes or plates waves can be studied with the help of propagation constant gg for these waves.

(a) Propagation Constant in parallel planes

γg  = √ K2gw2με

γg  = √(mπ /α)2 – w2με

Where                      Kg = mπ /α Continue reading “CHARACTERISTICS OF TRANSVERSE ELECTRIC AND TRANSVERSE ELECTRIC WAVES”

Transverse magnetic waves in parallel planes

 DEFINITION TRANSVERSE MAGNETIC (TM) WAVES OR E WAVES   :

In this case, the component of magnetic field vector H lies in the plane transverse to the direction of propagation that is there is no component of H along the direction of propagation where as component of electric field vector E lies along the direction of propagation.

Derivation transverse magnetic waves between parallel planes:

As the direction of propagation is assumed as z-direction, therefore,

Hz = 0, Ez not equals to 0

By substituting Hz = 0 in equation, we get

Hx = 0, Ey = 0,and Ex not equals to 0, Hy not equals to 0

Now write wave equation for free space in term of H Continue reading “Transverse magnetic waves in parallel planes”

Transverse electric waves

DEFINITION TRANSVERSE ELECTRIC (TE) WAVES OR H WAVES IN PARALLEL PLANES:

In the case, the component of electric field vector E lies in the plane transverse to the direction of propagation that is there is no component of E along the direction of propagation where as a component of magnetic field vector H lies along the direction of propagation.

Derivation of transverse electric waves in parallel planes:

As the direction of propagation is assumed as z-direction, therefore

Ez = 0 and Hz is not equal to 0

Now by substituting Ez = 0 in equation (8) of article “waves between parallel planes”, we get

Ex= 0 and Hy = 0 and

Ey not equals to 0 , H not equals to 0

Now write wave equations for free space in terms of E

Ñ2E =g2gE

= -w2μεE                     (because g2g = (jwμ) (σ + jwε) As σ =0(from                                                                            assumption  (c) of article “waves between parallel planes” => g2g =-w2με)

Or                    d2E/dx2 + d2E/dy2 + d2E/dz2 = -w2μεE

For the y component, the wave equation will become Continue reading “Transverse electric waves”

Waves between parallel planes

Let us discuss how waves propagate through parallel planes and derive the necessary relation of transverse electric and magnetic waves:

Assumptions :

(a)  Pair of parallel planes are perfectly conducting.

(b)  Separation between the planes is ‘a’ meter in x – direction.

(c)  Space between planes is perfect dielectric (σ = 0) of permittivity ε and permeability μ.

(d)  Planes are of infinite extent in the y and z direction. Continue reading “Waves between parallel planes”

Poynting theorem and derivation

Poynting Theorem

Statement. This theorem states that the cross product of electric field vector, E and magnetic field vector, H at any point is a measure of the rate of flow of electromagnetic energy per unit area at that point, that is

                                                P = E x H

Here P → Poynting vector and it is named after its discoverer, J.H. Poynting. The direction of P is perpendicular to E and H and in the direction of vector E x H Continue reading “Poynting theorem and derivation”

Electric Potential Due To Single Charge Or Point Charge

let us discuss and derive the electric potential due to single charge or point charge. We will calculate electric potential at any point P due to a single point charge +q at O ;where OP=r

Electric potential at P is the amount of work done in carrying a unit positive charge from ∞ to P.

At any point A on the line joining OP ,where OA=x,the electric intensity is E=1/4πε0q/x2 along OA produced (try to make the figure yourself). Continue reading “Electric Potential Due To Single Charge Or Point Charge”