^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.

^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.

^Transformer

Transformer is an electric device based on of mutual induction used to transfer power from the primary to the secondary by

convert low alternating voltage (at high alternating current) into high alternating voltage (at high alternating current) & vice versa without any transfer of charge. Its efficiency is defined as

k > 1 for a step up & k < 1 for a step down.

Because of energy losses like Flux loss, Cu- loss,

Fe – loss, Hysteresis loss, Humming noise, the efficiency of a transformer is never 100 %

^Motor starter

It is a variable resistor (maximum when the motor is just switched on & its value decreases gradually as the motor picks up the speed) used in the series of the armature to supply the constant current to the motor & thus to protect the motor from burning.

^LC R parallel circuit or rejecter circuit

Reciprocal of impedance Z is called admittance Y. Current delivered by the supply is I = I₁ + I₂

If the source oscillates at angular frequency  then imaginary part of Y becomes zero & Y is minimum. This stage is called resonance. Following points are of interest at resonance.

1. The reciprocal of the minimum value of Y is called the parallel or dynamic resistance, it is

2. Peak current through supply

3. Peak current through

4. Q – factor or current magnification i.e. the ratio of the peak current through supply to that through

5. Used as transmitting circuits.