Questions: Electromagnetic Waves

Q1. What is displacement current and why was it introduced?

Answer (English): The displacement current equals epsilon0 multiplied by the rate at which the electric flux through a surface changes, I_d = epsilon0 d(phi_E)/dt. Maxwell introduced it to remove a contradiction in Ampere's law. For a loop drawn around the charging wire of a capacitor, one surface bounded by the loop cuts the wire and encloses a conduction current, while another surface passes between the plates and encloses none, so the original law would predict different magnetic fields for the same loop. Maxwell added the displacement current, and then both surfaces give the same result. Physically it is the changing electric field between the plates, and it has the same strength as the conduction current in the wire.

Hinglish: Displacement current I_d = epsilon0 d(phiE)/dt hota hai. Ise Ampere ke law ki contradiction hataane ke liye introduce kiya gaya: charging capacitor ke wire ke around loop lo to ek surface wire ko cut karti hai aur conduction current ginti hai, doosri plates ke beech se jaati hai aur kuch nahi ginti, isliye same loop ke do jawab aa rahe the. Displacement current add karne se dono surface same result dete hain, aur ye plates ke beech ka changing electric field hai jiska strength wire ke current ke barabar hota hai.

Q2. State the four Maxwell equations in words.

Answer (English): The first is Gauss's law for electricity: the electric flux through a closed surface is equal to the charge enclosed divided by epsilon0. The second is Gauss's law for magnetism: the net magnetic flux through a closed surface is zero, because magnetic monopoles do not exist. The third is Faraday's law: a changing magnetic flux through a circuit induces an emf, which is equivalent to saying a changing magnetic field produces an electric field. The fourth is the Ampere Maxwell law: a magnetic field is produced by a conduction current and also by a changing electric flux, the two contributions adding on the right hand side.

Hinglish: Pehli Gauss ka electric law: closed surface se electric flux enclosed charge/epsilon0 hota hai. Doosri Gauss ka magnetism law: net magnetic flux zero, kyunki monopole nahi hote. Teesri Faraday ka law: changing magnetic flux se emf, yaani changing magnetic field electric field banata hai. Chauthi Ampere-Maxwell law: magnetic field conduction current aur changing electric flux dono se banta hai, dono contributions jud jate hain.

Q3. Write the properties of electromagnetic waves.

Answer (English): Electromagnetic waves are produced by accelerated charges and consist of oscillating electric and magnetic fields that are in phase, mutually perpendicular and perpendicular to the direction of propagation, so the waves are transverse. They travel in vacuum at c = 1 divided by the square root of mu0 epsilon0, which is 3 x 10 to the power 8 m per second, and require no medium. The ratio of the field amplitudes is E0/B0 = c, and in a medium the speed becomes c divided by the square root of the relative permittivity and permeability. They carry energy and momentum, exert radiation pressure, and show reflection, refraction, interference, diffraction and polarisation.

Hinglish: Electromagnetic waves accelerated charges se banti hain, inme oscillating electric aur magnetic fields hote hain jo in phase, ek doosre ke perpendicular aur propagation direction ke perpendicular hote hain, isliye wave transverse hai. Vacuum mein speed c = 1/root(mu0 epsilon0) = 3 x 10^8 m/s, koi medium nahi chahiye. E0/B0 = c hota hai, medium mein speed c/root(mu_r epsilon_r) ban jati hai. Ye energy aur momentum le jati hain, radiation pressure deti hain, aur reflection, refraction, interference, diffraction aur polarisation dikhati hain.

Q4. How is the speed of light related to mu0 and epsilon0?

Answer (English): Maxwell's equations predict that a disturbance in the electric and magnetic fields travels with speed equal to one divided by the square root of the product of the permeability of free space and the permittivity of free space. Substituting mu0 = 4 pi x 10 to the power minus 7 and epsilon0 = 8.85 x 10 to the power minus 12 gives 3 x 10 to the power 8 m per second, the measured speed of light. This agreement was the evidence that light is an electromagnetic wave. In a medium the speed is c divided by the square root of the product of the relative permeability and relative permittivity, so the speed is lower than c in any material medium.

Hinglish: Maxwell ki equations batati hain ki field disturbance ki speed 1/root(mu0 epsilon0) hoti hai. mu0 = 4 pi x 10^-7 aur epsilon0 = 8.85 x 10^-12 daalne par 3 x 10^8 m/s milta hai, jo light ki measured speed hai. Yahi proof tha ki light electromagnetic wave hai. Medium mein speed c/root(mu_r epsilon_r) hoti hai, isliye kisi bhi material mein speed c se kam hoti hai.

Q5. A wave has E0 = 900 V per metre. Find B0 and the intensity if the wave travels in vacuum.

Answer (English): In vacuum E0/B0 = c, so B0 = 900/(3 x 10^8) = 3 x 10 to the power minus 6 T, that is 3 microtesla. The average energy density is epsilon0 E0 squared, which is 8.85 x 10^-12 x 810000 = 7.17 x 10^-6 J per cubic metre. The intensity is this energy density times c, giving about 2.15 x 10^3 W per square metre. These are the standard steps: amplitude ratio first, then energy density, then intensity by multiplying by c.

Hinglish: Vacuum mein E0/B0 = c, isliye B0 = 900/(3 x 10^8) = 3 x 10^-6 T, yaani 3 microtesla. Average energy density epsilon0 E0^2 = 8.85 x 10^-12 x 810000 = 7.17 x 10^-6 J/m^3 hoti hai. Intensity energy density x c = lagbhag 2.15 x 10^3 W/m^2 milti hai. Steps yaad rakho: pehle amplitude ratio, phir energy density, phir intensity.

Q6. Why do electromagnetic waves carry momentum and what is radiation pressure?

Answer (English): The fields of an electromagnetic wave carry energy, and relativity associates a momentum with any energy in motion, equal to the energy divided by c. When the wave is absorbed by a surface, that momentum is transferred, and the force per unit area is the radiation pressure. For complete absorption the pressure is the intensity divided by c, and for complete reflection it is twice as large, because the momentum reverses direction. The effect is small for ordinary light but is used in solar sails and is measurable for intense laser beams.

Hinglish: Wave ke fields energy le jate hain, aur moving energy ke saath momentum judta hai jo energy/c hota hai. Surface par wave absorb hone par momentum transfer hota hai aur force per unit area radiation pressure kehlata hai: complete absorption par intensity/c, complete reflection par 2I/c. Aam roshni mein effect chhota hota hai par solar sail aur laser beams mein use hota hai.

Q7. Arrange the electromagnetic spectrum in order and name one use of each band.

Answer (English): From longest wavelength to shortest, the order is radio waves, microwaves, infrared, visible, ultraviolet, X-rays and gamma rays. Radio waves are used for broadcasting and communication, microwaves for radar and microwave ovens, infrared for remote controls and heating, visible light for sight and photography, ultraviolet for sterilising and LASIK surgery, X-rays for medical imaging and crystal structure studies, and gamma rays for cancer treatment and sterilising equipment. All bands travel at the same speed c in vacuum, and the boundaries between them are not sharp.

Hinglish: Longest se shortest order: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma. Radio broadcasting aur communication ke liye, microwave radar aur oven ke liye, infrared remote aur heating ke liye, visible sight aur photography ke liye, ultraviolet sterilising aur LASIK ke liye, X-rays imaging aur crystal study ke liye, gamma rays cancer treatment ke liye use hoti hain. Vacuum mein sab ki speed c hoti hai aur bands ke beech sharp boundary nahi hoti.

Q8. How is the displacement current related to the conduction current in a charging capacitor?

Answer (English): They are equal at every instant. If the charge on the plates is q, the field between the plates is sigma/epsilon0, so the electric flux is q/epsilon0. The displacement current is epsilon0 times the rate of change of this flux, which gives dq/dt, the rate at which charge is arriving on the plates. That is exactly the conduction current in the wire. This equality is what makes the circuit continuous: the conduction current in the wire continues between the plates as a displacement current and reappears as a conduction current on the other side.

Hinglish: Dono har instant barabar hote hain. Plates par charge q ho to field sigma/epsilon0 hota hai aur electric flux q/epsilon0. Displacement current epsilon0 x d(flux)/dt = dq/dt hota hai, jo wire ke conduction current ke barabar hai. Isi equality se circuit continuous lagta hai: wire ka current plates ke beech displacement current ban kar doosri side phir conduction current ban jata hai.

Q9. What happens to the speed, wavelength and frequency of an electromagnetic wave when it enters a dielectric medium?

Answer (English): The frequency is set by the source and does not change when the wave enters a new medium. The speed becomes c divided by the square root of the product of the relative permittivity and the relative permeability, so it decreases for a dielectric. Since the wavelength is the speed divided by the frequency, a lower speed with the same frequency means a shorter wavelength. For a medium with relative permittivity 3/2 and relative permeability 8/3, the product is 4, so the speed halves, the wavelength halves, and the frequency stays the same.

Hinglish: Frequency source se tay hoti hai, medium badalne par nahi badalti. Speed c/root(mu_r epsilon_r) ho jati hai, isliye dielectric mein kam ho jati hai. Wavelength = speed/frequency, isliye same frequency par kam speed ka matlab chhoti wavelength. Agar epsilon_r = 3/2 aur mu_r = 8/3 ho to product 4 hota hai, speed aadhi, wavelength aadhi, aur frequency wahi.

Q10. Why is it said that the Maxwell equations predicted electromagnetic waves before they were discovered?

Answer (English): The four equations show that a changing electric field produces a magnetic field and a changing magnetic field produces an electric field. If a disturbance is created, the two effects keep regenerating each other and the disturbance propagates through space at the speed 1 divided by the square root of mu0 epsilon0. Maxwell calculated this speed from constants measured in electrical and magnetic experiments, obtained 3 x 10 to the power 8 m per second, and recognised it as the speed of light. That was a prediction of waves that had not been produced or detected, and Hertz confirmed them experimentally in 1887.

Hinglish: Chaar equations dikhati hain ki changing electric field magnetic field banata hai aur changing magnetic field electric field. Disturbance banane par dono effects ek doosre ko regenerate karte hain aur wave 1/root(mu0 epsilon0) speed se aage badhti hai. Maxwell ne electrical aur magnetic constants se speed nikaali, 3 x 10^8 m/s mili, aur pehchana ki ye light ki speed hai. Ye un waves ki prediction thi jo tab tak produce ya detect nahi hui thi, aur Hertz ne 1887 mein experiment se confirm kiya.

Quiz below: five questions on displacement current, wave properties, the speed relation and the spectrum. Revise the spectrum table before you start.