^Total energy density of EM waves
^Total energy density of EM waves
Total energy (u) of EM waves
,
^Magnetic energy density of EM waves
^Magnetic energy density of EM waves
Magnetic energy density (uB) of EM waves is
^Electric energy density of EM waves
^Electric energy density of EM waves
Electric energy density (uE) of EM waves is
^Speed of EM-waves
^Speed of EM-waves
Speed of EM wave depends only upon the electric and magnetic properties of medium & is given by
^Equation of EM-waves
^Equation of EM-waves
For an EM wave propagating along + X-axis is described by the mathematical functions
EY = E0 sin (ωt – kx), EX = 0 & EZ = 0 &
BZ = B0 sin (ωt – kx), BX = 0 & BY = 0
^Propagation of EM-waves
^Propagation of EM-waves
EM waves propagate such that E & B vectors
1. are always in phase
2. vary sinusoidally at right angles to each other as well as it right angles to direction of (DOP) & thus EM waves are transverse.
DOP is in the direction given by 
^Deflection of EMwaves
^Deflection of EM-waves
EM waves are neutral, thus can’t be deflected by E & B fields.
^History of EM waves
^History of EM waves
In 1865 Maxwell predicted the existence of electromagnetic waves purely from theoretical consideration. He showed that an accelerating charge produce EM waves of wave frequency as that of the oscillating charge.
In 1887, Hertz succeeded in experimentally confirming the existence of em waves. He sued an oscillatory LC circuit for producing these waves he was able to produce and detect e.m. waves of wavelength around 6 m.
In 1885 J.C. Bose succeeded in producing EM wave of much shorter wavelength (5 mm to 25 mm) with the help of a self designed radiator. He was able to transmit EM waves over a distance of about 20 m.
In 1896 Marconi, succeeded in transmitting EM waves across the British Channel in 1899 and across the Atlantic ocean in 1901. His experiments marked the beginning of radio communication.
^Generating EM waves
^Generating EM waves
Maxwell suggested an accelerating charge produces EM waves. An electric charge oscillating harmonically with time produces an oscillating electric field in its neighbourhood & this field in turn produces an oscillating magnetic in the neighbourhood. The process continues because the oscillating electric and magnetic fields act as sources of each other & hence an EM wave originates from the oscillating charge. The frequency of the EM wave is equal to the frequency of oscillation of the charge. The energy carried by the wave comes from the source which makes the charge oscillating. To generate an EM wave of frequency f, we need to set up an ac circuit in which the current oscillates at the frequency f. It is easier to generate low frequency EM waves such as a radio wave than to produce high frequency EM waves. e.g. the generation of yellow light requires an oscillator of frequency 6 x 1014 Hz, while the modern oscillators have frequency not above 1011 Hz.
^Maxwell law
^Maxwell law
Just as Faraday’s law tells us that a time-varying magnetic field produces an electric field, the Ampere-Maxwell law predicts that a time-varying electric field produces a current & magnetic field.
This current is called Maxwell displacement current.
Let 
is the rate of change of electric flux of through the area bounded by the closed curve along which the circulation of 
is calculated, then Maxwell -Ampere law is expressed as
Here 
is called the displacement current.
Consider a uncharged parallel-plate capacitor connected to a battery through a switch. On closing the switch the charge on capacitor plates increases, which increases the electric field & electric flux linked with any imaginary loop considered parallel to the area of capacitor plates. This induces a displacement current in the direction of electric field, the magnetic field due to this current is calculated using the AML i.e.
If the capacitor plates has vacuum, then the conduction current will be zero, however due to displacement current the magnetic field at a point on the surface of loop L will be 
If a loop is situated at r = R, then 
If a loop is situated at r > R, then the loop encloses a displacement current equal to conduction current & the magnetic field becomes 
.
Also a compass needle place any where around a connecting wires or in the capacitor spacing deflects till the capacitor is undergoing charging or discharging.
