HC Verma Class 12 Physics Solutions Chapter 40: Electromagnetic Waves

About the chapter: HC Verma Solutions Class 12 Physics Chapter 40

Let’s talk about electromagnetic waves, what they are and how they work, and how we can use them in our everyday lives. Communication is one of the most important ways electromagnetic waves are used.

Here are some of the most important ways electromagnetic waves are used:

• Electromagnetic waves make it possible for us to see everything around us.
• These waves help planes find their way and help the pilot land and take off without any trouble. They also help figure out how fast an airplane is going.
• In medicine, these waves are used in very important ways. In laser eye surgery and x-rays, for example.
• Signals for radio and TV are sent through the air with the help of electromagnetic waves.
• Electromagnetic waves help figure out how fast vehicles are going.
• They are used in things like TV remotes, remote-controlled cars, LED TVs, microwave ovens, and so on.
• Electromagnetic waves make it possible for cell phones to send and receive voices.

Maxwell’s Experiments

• Maxwell said that magnetic fields can be made by electric fields that change over time.
• On the other hand, the Faraday-Lenz law says that an electric field is made when a magnetic field changes over time.
• Faraday-law Lenz’s says that an EMF is caused in a circuit when the amount of magnetic flux in that circuit changes.
• Because of this, there is an electric field around the electric current that flows through the circuit.
• Now, when Maxwell saw this, he said that the opposite must also be true. That is, an electric field that changes over time must also be able to make a magnetic field.

Ampere’s Circuital Law

• Ampere’s circuital law says that the length element of the magnetic field is equal to 0 times the total current going through the surface. dl=0l is a math equation.
• Maxwell, on the other hand, found some problems with Ampere’s law.
• So, Ampere’s circuital law wasn’t always right. It was only right sometimes.
• Maxwell came to this conclusion after looking at different situations. For example, he took a capacitor and tried to figure out where the magnetic field was in a certain part of it.
• As shown in the figures below, he found the value of B at point P, assuming that some current I was flowing through the circuit.

He thought about 3 different loops, as shown in the figures below. If Ampere’s law about circuits was right, it should work for all three of these.

Case 1: Maxwell thought about a surface with a radius of r and a length of dl. Ampere’s circuital law says that;

• ∫B.dl=μ0l
• ⇒B(2πr)=μ0l
• ⇒B=μ0l2πr

Case 2: Maxwell thought of a surface like the top of a box that was open and used Ampere’s circuital law;

• ∫B.dl=μ0l
• Here, the current, I, turned out to be zero because there was no current flowing through the capacitor.
• ⇒∫B.dl=0

Case 3: Maxwell thought about the area between the two plates of a capacitor.

• In this case, I is also 0, so B is also 0.
• Maxwell found that the values of magnetic fields are not the same at the same point but with different Amperial surfaces. This shows that his claims about inconsistencies in the law are true.
• Maxwell pointed out that Ampere’s circuital law had some flaws. He fixed them and made sure that Ampere’s circuital law worked the same way in all of them.

The change Maxwell made to Ampere’s Law

Ampere’s law says that if the electric field inside the loop stays the same, the line integral of the resultant magnetic field along a closed plane curve is equal to 0 times the total current flowing through the area bounded by the closed curve.

• This rule only worked for steady currents.
• Maxwell found the flaws in Ampere’s law and changed it to include electric fields that change over time.
• Maxwell thought that for Ampere’s circuit law to be true, there must be some current between the plates of the capacitor.
• The flow of electrons caused current to flow outside of the capacitor.
• There was no flow of electricity between the capacitor’s plates.
• Maxwell said that there should be an electric field between the plates of the capacitor. This field should go from the positive plate to the negative plate.
• How big the electric field is, E = (V/d)
• Where V = the difference in charge between the plates
• d=the distance between the plates
• ⇒E=(Q/Cd)
• Where, Q = the charge on the capacitor’s plates,
• ⇒E=(Q/ (Aε0d/d))
• ⇒E=Q/(Aε0)
• Where A = the capacitor’s surface area. 

HC Verma Solutions Class 12 Physics Complete Syllabus

• Chapter 23 – Heat and Temperature
• Chapter 24 – Kinetic Theory of Gases
• Chapter 25 – Calorimetry
• Chapter 26 – Laws of Thermodynamics
• Chapter 27 – Specific Heat Capacities of Gases
• Chapter 28 – Heat Transfer
• Chapter 29 – Electric Field and Potential
• Chapter 30 – Gauss’s Law
• Chapter 31 – Capacitors
• Chapter 32 – Electric Current in Conductors
• Chapter 33 – Thermal and Chemical Effects of Current
• Chapter 34 – Magnetic Field
• Chapter 35 – Magnetic Field due to a Current
• Chapter 36 – Permanent Magnets
• Chapter 37 – Magnetic Properties of Matter
• Chapter 38 – Electromagnetic Induction
• Chapter 39 – Alternating Current
• Chapter 40 – Electromagnetic Waves
• Chapter 41 – Electric Current through Gases
• Chapter 42 – Photoelectric Effect and Wave-Particle Duality
• Chapter 43 – Bohr’s Model and Physics of Atom
• Chapter 44 – X-rays
• Chapter 45 – Semiconductors and Semiconductor Devices
• Chapter 46 – The Nucleus
• Chapter 47 – The Special Theory of Relativity

Features of Utopper HC Verma Solutions Class 12 Physics Chapter 40

• Students can solve similar problems on their own with the help of HC Verma’s answers in the Utopper.
• Students are given answers that are correct and easy to understand.
• The solutions are given to match the level of understanding of a student in that class.
• The HC Verma solutions that Utopper gives the answer to and explains all of the questions in each chapter.