Maxwell’s Equations and Sources of EM Waves, Practice Problems, FAQs

Do you know how we receive energy from the sun on the earth? Without this energy, the existence of living beings on the earth would not have been possible. Actually we receive this energy in the form of radiation from the sun. Now you must be wondering, as there is no medium in between earth and sun how does this energy reach on the earth. These radiations are electromagnetic waves so they do not require medium to travel. Electromagnetic waves are also known as EM waves. EM waves are generated when a charged particle is accelerated or when an electron jumps from higher state to lower state. Electromagnetic waves are solved by Maxwell's equations, which are the fundamental equations of electrodynamics. Let's take a closer look at EM waves.

Table of Contents

• Maxwell Equations
• Sources of EM Waves
• Properties of EM Waves and Important Relation
• Practice Problems
• FAQs

Maxwell Equations

Maxwell was the first to discover that the propagation speed of electromagnetic waves is the same as the speed of light, leading to the conclusion that EM waves and visible light are equivalent. Electric field E and magnetic field B are related by Maxwell's equations to their sources which are basically electric charges and current. Maxwell's equations in free space are as follows:

1.  This equation represents Gauss's law in electrostatics. Which It states that the net electric flux through any closed surface is equal to times the total charge enclosed by the that surface. This law relates the electric fields with the charge distribution. The Gauss law has been empirically verified to be equal to Coulomb's inverse square law.

In the above figure you can see that charge is placed inside closed surface . Electric field is shown as .

2. The equation This equation is considered as the Gauss's law in magnetism. The net magnetic flux travelling through a closed surface is zero, according to this formula. It implies means that the number of magnetic field lines entering the closed surface is equal to and the number of magnetic lines leaving the closed surface are the same. That means the magnetic field does not start or end at a point. therefore there Thereare is no isolated magnetic monopoles monopole.

From the above figure you can see that magnetic field lines form closed loops. So the number of field lines entering and leaving the surface are the same. So magnetic flux is zero. 

3.  This equation is Faraday's law of electromagnetic induction. This law relates electric fields to changing magnetic flux. "This equation is confirmed by induced current in a conducting loop put in an area where the magnetic field is changing with time."

As shown in the above figure, if we move the magnet towards the coil then magnetic flux through the coil will increase. Because of the change in magnetic flux EMF will be induced in the coil which can be observed as shown in the figure.

4.  This equation represents the Ampere-Maxwell's law or generalised form of Ampere's law. This law It states that the line integral of the magnetic field along a closed loop is equal to times the total current threading passing through the area which is bounded by the closed loop". This law describes how a magnetic field can be produced by both changing electric flux and a conduction current. the process of how a magnetic field can be produced by a changing electric flux and a conducting current.

Figure shows the magnetic field produced due to the current carrying conductor. According to Ampere’s Law the line integral of magnetic field is equal to the times the net current inside the loop. 

Note: Maxwell's equations are as important to the study of electromagnetic phenomena as Newton's laws are to mechanical phenomena. The fact that Maxwell's equations may be utilised to establish the law of charge conservation is a significant benefit.

Electromagnetic waves or electromagnetic radiation are waves created by accelerated charged particles and consist of electric and magnetic fields vibrating transversely and sinusoidally perpendicular to one another and to the propagation direction.

These waves are produced in by the following physical phenomena:

• When an electric charge is at rest, it generates simply electrostatic fields.
• A charge travelling at a constant pace (i.e. steady current) generates both an electric and magnetic field; however, the magnetic field does not change with time, hence the electric field is not time changing.
• Electromagnetic waves are formed when an accelerating charge creates both an electric and magnetic field that fluctuates with location and time.
• In the case of LC oscillation, an accelerating charge creates electromagnetic waves with the same frequency as the accelerating charge (i.e., frequency of oscillating LC circuit)
• Electromagnetic waves are not emitted by an electron in a fixed orbit around its nucleus. It will only emit during the transition from a higher to a lower energy orbit.
• When a fast electron collides with a target with a high atomic weight, electromagnetic waves (X-ray) are created.
• When a nucleus is de-excited in radioactivity, electromagnetic waves (-rays) are created.

Properties of EM Waves and Important Relation

• EM waves are produced by accelerated charge and oscillating charge oscillating charge and accelerated charge.
• It travels through free space (vacuum) with a speed equal to which is given by .
• These waves do not don’t require material for their propagation. 
• Electric and magnetic fields vary sinusoidally. become maximum at the same place and at the same time simultaneously with respect to time and place. So the phase difference between is zero.
• are perpendicular to each other. as well as to the direction of propagation. Direction of propagation can be determined by .
• Amplitude of are related to speed of wave propagation as .
• Velocity of an EM wave does not depend on the amplitudes of electric and magnetic fields. It is decided by the electric and magnetic properties of the medium. Speed of an electromagnetic wave in a medium is
• Energy carried by an electromagnetic waves is equally divided between electric field and magnetic field. Total average energy density
• Electromagnetic waves are not deflected by electric or magnetic fields because they do not have any charged particles.

Practice Problems

Q. Determine whether or not the following statement is correct: Radio waves and X-rays are both electromagnetic waves that travel at the same rate, right?

A. The claim made is correct. For all waves in the electromagnetic spectrum, the speed of light remains constant. The frequency, energy, and wavelength of waves vary based on the type of wave and the source that creates it. The velocity, on the other hand, remains constant.

Q. How does the medium through which an electromagnetic wave passes impact its properties?

A. The medium through which an electromagnetic wave passes determines its velocity. The source determines other elements of the wave, such as frequency, time period, and wavelength.

Q. What is the reason for the magnetic field line forming a continuous closed loop?

A. Magnetic lines generate continuous closed loops because magnetic monopoles do not exist in nature. Magnetic poles, North and South, are always found paired together in such a way that field lines beginning at one pole end at the other, forming a complete loop. The third equation of Maxwell explains this.

Q. What is the third equation of Maxwell?

A. Maxwell's third equation is A. Faraday's Law. According to the idea, a changing magnetic field creates an electric field. On the right side of the equation, a changing magnetic field is shown. When the magnetic field changes, a current flows in a loop through which the magnetic field passes. EMF may be created in a closed loop by changing the magnetic flux within the loop.

FAQs

Q. What are the explanations for Maxwell's Equations?
A. It shows how electric charges and currents produce magnetic and electric fields. The equations of Maxwell illustrate how an electric field may create a magnetic field, and vice versa.

Q. How does the frequency of UV rays change when it travels from air to glass?
A. Frequency of UV rays is the property of source. It does not depend on the medium. So frequency remains constant. 

Q. What does the first equation of Maxwell tell us?
A. Maxwell's first equation is based on the Gauss law of electrostatics, which states that "when a closed surface integral of electric flux density is always equal to charge contained across that surface."

Q. Can a time-varying electromagnetic field be generated by a uniform current carrying wire?
A. A uniform current carrying wire creates both an electric and magnetic field; however, the magnetic field does not vary with time, hence the electric field is not time variable.