Electromagnetic Waves Class 12 | Chapter 8 | Physics | Term 2 |

Electromagnetic Waves Class 12 | Chapter 8 | Physics |

Introduction

We have read in previous chapters that electric current produces magnetic field and also that the two current carrying wires exert a magnetic force on each other and magnetic field changing with time gives rise to an electric field. But, does electric field changing with time produces magnetic field?

The answer is, yes. James Clerk Maxwell proposed that, indeed this was the case, not only an electric current but also a time varying electric field generates magnetic field.

He formulated a set of equations that includes electric and magnetic fields, and their sources, the charge and current densities these equations are known as Maxwell’s equations.

The most important Indication to emerge from Maxwell’s equation is the existence of electromagnetic waves, which are () time varying electric and magnetic fields that propagate in space. The speed of these waves turned out to be very close to the speed of light i.e. 3×108 m/s. Proving that light is an electromagnetic wave.

DISPLACEMENT CURRENT

The change in electric field with respect to time produces current ,known as displacement current.To see this let’s consider the process of charging a capacitor. According to a circuital law (chapter 4).

Here, we have to find the field on the point p just outside the capacitor. Considering a circular loop with radius r perpendicular to the direction of the current carrying wire.The field is, symmetrically, directed along the circumference of the loop and is same in the magnitude at all the points.If b is the magnitude of the field and the circumference is 2πr, therefore,

Now, if we consider another port like surface which has it’s bottom between the capacitor plates. Also another subsurface which is shaped like a tiffin box (without the lid). On applying ACL, we will find that the left side of the above equation is not changed at the right side have become 0 instead of U0i.Therefore we know that is missing from the Ampere’s Law. To find this term let’s take in consideration the electric field between two plates. Let the charge be Q and the area A the magnitude of the field is,

The flux through the surface is—

If there is any current through the surface of capacitor, it can be expressed as i=dQ/dt,

This value is the missing term from the Ampere’s Law and it is known as displacement current id ,

Key Points:
1. Conduction current is the total current carried by the conductor due to the flow of charges.
2. The total current is the sum of conduction current and displacement current—

3. There are regions in which there is no induction or displacement current for e.g. between the platesof charging/discharging capacitor.
4. Also, there are regions in which there is no displacement current but conduction current is present for e.g. A wire carrying steady current and also outside a capacitor.
**Conduction current is only present outside the capacitor while the displacement current present inside it.
The correct or generalized Ampere’s Law is given as, “the total current interview any surface of which the closed loop is the perimeter is the sum of of conduction and displacement current”—

Maxwell’s Equations
Sources of Electromagnetic Waves

Neither stationary charges nor charges in uniform motion can be sources of electromagnetic waves. These waves are generated by accelerated charges. Consider a charge oscillating with some frequency (oscillating charge is an example of accelerated charge). This produces an oscillating electric field in the space which in turn producers magnetic field and this osculating magnetic field again produces electric field and so on.These accelerating electric and magnetic field regenerate each other, as the wave propagates through the space.The frequency e of electromagnetic wave is equal to the frequency of oscillation of charge.

Related

Properties of Electromagnetic Waves

1. Electromagnetic waves do not require a medium to propagate — There is no material medium required for the vibration of electric and magnetic field.
2. These waves can be polarized.
3. Electromagnetic waves carry energy and momentum — electromagnetic waves carry electric and magnetic field, they must have some energy associated with them. The magnitude of the momentum p can be expressed as,

4. Electromagnetic waves exert pressure — These waves carry momentum, therefore, they exert pressure. This pressure is known as radiation pressure.
5. The speed of electromagnetic waves in free space or vacuum the fundamental constant i.e. 3×108 m/s.

Nature of Electromagnetic Waves

• Electric and magnetic field in an EMW areperpendicular to each other and to the direction of propagation.
• Both electric and magnetic field oscillates in phases with each other and the direction of energy transfer(velocity of wave) is given by E × B.
Consider a wave travelling in the z direction then the electric field Ex is in the X direction and the magnetic field By is in the Y direction.

We can write this as,
Where K is the wave number, given by,
And the speed of propagation of wave is given by,

Also, from Maxwell’s equations, we can conclude that,

Velocity of electromagnetic wave in any medium—
– It does not depend on electric and magnetic field but only depends on the properties of the medium.

Electromagnetic Spectrum

The classification of electromagnetic waves on the basis of the frequency is known as electromagnetic spectrum.
Different types of waves are classified as—

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