Class 12 Electromagnetic Waves Notes
So, what are electromagnetic waves?
Electromagnetic (EM) waves are those that are affected by both electricity and magnetism. Because they are waves connected with electricity and magnetism, they would almost certainly propagate across space.
These waves are essentially linked to time-varying electric and magnetic fields that travel over space. Electromagnetic waves are created when electric and magnetic fields interact and change over time.
Maxwell’s equations are used to develop electromagnetic equations. Maxwell determined that these EM waves had several specific qualities that may be used for a variety of practical applications.
Current Displacement The current that comes into play in the region where the electric field and electric flux change over time. It is provided by
Current Demand for Displacement Ampere’s circuital equation for conduction current during capacitor charging was discovered to be incoherent. As a result, Maxwell altered Ampere’s circuital law. The displacement current is produced in space as a result of a change in the electric flux associated with the surface. This demonstrates that the source of the magnetic field is a fluctuating electric field.
Experiments by Maxwell:
1) Maxwell proposed that magnetic fields can be generated by time-varying electric fields.
2) Faraday-Lenz law, on the other hand, states that a time-varying magnetic field creates an electric field.
3) An EMF is produced in a circuit by the Faraday-Lenz equation whenever the quantity of magnetic flux associated with that circuit varies.
4) As a result, an electric current is created in the circuit, which is connected to an electric field.
5) When Maxwell discovered this, he asserted that the converse must also be true, i.e., a time-varying electric field must likewise be capable of producing a magnetic field.
The line integral of the magnetic field across the length element is equal to μ0 times the total current travelling through the surface, according to Ampere’s circuital equation. Mathematically, ∫dl=μ0l
However, Maxwell discovered certain flaws in Ampere’s circuital law. As a result, Ampere’s circuital law was discovered to be valid in certain situations but not always. Maxwell examined several circumstances to get to this conclusion. He took a capacitor, for example, and attempted to determine the magnetic field at a given place in a section of this capacitor. He computed the value of B at point P, as shown in the following figures, assuming some current I flowing through the circuit. He investigated three distinct loops, as seen in the images below.
Maxwell considered a surface of radius r and a circumference dl. Ampere’s circuital law states;
∫B.dl=μ0l
B(2πr)=μ0l
B=μ0l2πr
Maxwell applied Ampere’s circuital law to a surface, such as a box with its lid open.
∫B.dl=μ0l
Here, as there is no current flowing inside the capacitor, the current, turned out to be zero.
⇒∫B.dl=0
Maxwell considered the surface presented between two plates of a capacitor. In this situation, too, I=0, and so B=0.
The direction of the electric field is perpendicular to the surface of the plate of the capacitor.
Now, as E=0 outside the plates and
E=(Q/(Aε0)), there might be the presence of some electric field between the plates.
Electric flux flowing through the surface
=ΦE=(EA)=(QA)/(Aε0)=(Q/ ε0)
Taking Q as a charge on the capacitor which changes with time, the current will get generated. Therefore, the current generated is given by the equation
Id=(dQ/dt)
Where,
Id= displacement current
Because Maxwell was able to remedy the flaws in Ampere’s circuital law, the law became known as Ampere-Maxwell law from then on.
Conduction current is the current that occurs as a result of the passage of charges. It is represented by Ic.
Displacement current is the current that emerges as a result of a change in the electric field. It is represented by Id.
- Ampere-Maxwell law stated that
∫dl=μ0(Ic+Id)
⇒∫dl=μ0Ic+μ0ε0(dΦE/dt)
So, What are the consequences of the Ampere-Maxwell Law?
- Case 1: Magnetic field is given by
∫dl=μ0Ic
⇒∫dl=μ0Ic/2πr
- Case 2: Magnetic field is given by
∫dl=μ0Id
⇒∫dl=μ0Id/2πr
So, these facts are the conclusion.
In both circumstances, the value of B is the same and the total current must be constant. The Ampere-Maxwell law creates a magnetic field from a time-varying electric field. In the first phase, an electric field exists between the plates, and this electric field varies with time. As a result, a displacement current exists, and this displacement current generates a magnetic field.
Faraday-Lenz’s law creates an electric field from a time-varying magnetic field. When an electric field changes over time, it creates a magnetic field, and when a magnetic field changes over time, it generates an electric field.
The Characteristics of Electromagnetic waves are that they are Transverse waves are EM waves.
Transverse waves occur when the direction of disturbance or displacement in the medium is perpendicular to the direction of wave propagation.
The particles of the medium in such a wave travel perpendicular to the wave’s propagation direction.
If the electromagnetic wave propagates along the x-axis, the electric and magnetic fields are perpendicular to the wave propagation.
This means that while wave propagation is on the x-axis, the electric field is on the y-axis, and the magnetic field is on the z-axis.
EM waves are transverse waves in nature.
The electric field of an EM wave is now given by Ey= E0sin(kxt) E y = E 0 sin ( k x t )
Ey is the electric field present along the y-axis
The Potential energy is given by p= U/c, where U is the total energy conveyed by electromagnetic waves and c is the speed of the electromagnetic wave.
The electromagnetic spectrum is the systematic sequential dispersion of electromagnetic waves in ascending or decreasing order of frequency or wavelength. The range extends between 10-12 m and 104 m, or from -rays to radio waves.
Important Fundamentals of electromagnetic wave applications are as follows:
Radio waves I Used in radio and television transmission.
(ii) In the realm of astronomy.
Microwaves are used in RADAR communications.
(ii) In molecular and atomic structure analysis.
(iii) For cooking.
Infrared rays are useful for determining molecular structure. (ii) In TV VCR remote control, etc.
UV rays are used in (i) burglar alarms. (ii) To eliminate germs and microorganisms in minerals.
X-rays (i) are Used in medical diagnostics since they travel through the muscles rather than the bones.
(ii) Detecting defects, fractures, and other flaws in metal products,
γ-rays I Food preservation. (ii) Radiation treatment.
The optical effect is caused by the electromagnetic waves’ electric field vector.
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