Class 12 Physics · Original EZT practice
Electromagnetic Waves (Class 12 Chapter 8): summary and practice
Electromagnetic Waves completes the field story: Maxwell's displacement current fixes Ampere's law, accelerated charges radiate transverse waves travelling at c, and the spectrum runs from radio waves to gamma rays with a use for every band. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 21 October 2026:
1. Displacement current and the Ampere-Maxwell law
A charging capacitor carries conduction current to its plates but none between them - yet a magnetic field appears there anyway. Maxwell fixed the gap with displacement current, i_d = epsilon0 d(phi_E)/dt, the time-varying electric flux acting as a source of magnetic field. The corrected Ampere-Maxwell law adds it to the conduction current.
2. Nature of electromagnetic waves
An EM wave carries perpendicular E and B fields that are in phase with each other and both perpendicular to the direction of travel. The speed in vacuum is c = 1/sqrt(mu0 epsilon0) = 3 x 10^8 m/s, and the amplitudes obey E0/B0 = c.
3. Sources of electromagnetic waves
Accelerated charges radiate: an oscillating charge launches a wave at its oscillation frequency. A steady current or a charge at rest radiates nothing - it is the acceleration that shakes the field loose.
4. The spectrum: radio to visible
Radio waves (metres and beyond) carry broadcasts; microwaves (centimetres) run radar, ovens and phones; infrared warms and images in the dark; visible light occupies the narrow slice our eyes detect. Wavelength falls and frequency rises as you move along the list.
5. Ultraviolet, X-rays and gamma rays
Ultraviolet tans, sterilises and is largely absorbed by ozone; X-rays image bones and luggage; gamma rays, the shortest and most energetic, come from radioactive nuclei and treat tumours. The high-frequency end ionises, which is why it is both useful and hazardous.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
From electric to magnetic amplitude
Choose the method: B0 = E0 / c.
EZT practice question
A plane electromagnetic wave has electric amplitude E0 = 6.3 V/m. Find its magnetic amplitude B0.
Show the worked solution
- B0 = E0 / c.
- = 6.3 / (3 x 10^8).
Answer: B0 = 2.1 x 10^-8 T.
Check: The magnetic amplitude is tiny in tesla because c is huge - that ratio is always E0 divided by 3 x 10^8.
Watch for this: Do not multiply by c - the magnetic amplitude is the SMALLER one, E0/c.
Now try it yourself
A wave with E0 = 120 V/m. Magnetic amplitude?
Check your answer
4 x 10^-7 T.
120 / (3 x 10^8) = 4 x 10^-7 T.
Convert frequency to wavelength
Choose the method: lambda = c / f.
EZT practice question
A shortwave radio band runs from 7.5 MHz to 12 MHz. Find the corresponding wavelength range.
Show the worked solution
- lambda = c / f.
- 7.5 MHz: 3 x 10^8 / 7.5 x 10^6 = 40 m.
- 12 MHz: 3 x 10^8 / 1.2 x 10^7 = 25 m.
Answer: 40 m down to 25 m - higher frequency means shorter wavelength.
Check: The product f x lambda stays fixed at c, so the band edges flip order: the low frequency gives the long wavelength.
Watch for this: Keep megahertz as 10^6 Hz - mixing MHz with metres without converting wrecks the answer.
Now try it yourself
A 30 MHz signal. Wavelength?
Check your answer
10 m.
3 x 10^8 / 3 x 10^7 = 10 m.
Size a microwave
Choose the method: lambda = c / f, with GHz = 10^9 Hz.
EZT practice question
A microwave link operates at 3 GHz. Find its wavelength.
Show the worked solution
- lambda = c / f.
- = 3 x 10^8 / 3 x 10^9.
Answer: 0.1 m, that is 10 cm.
Check: Centimetre-scale wavelengths are exactly why these are called microwaves - small compared with radio, long compared with light.
Watch for this: GHz is 10^9, not 10^6 - a thousand MHz.
Now try it yourself
A 10 GHz radar. Wavelength?
Check your answer
0.03 m (3 cm).
3 x 10^8 / 10^10 = 0.03 m.
Displacement current in a capacitor
Choose the method: Between the plates, i_d = epsilon0 d(phi_E)/dt equals the conduction current feeding the capacitor.
EZT practice question
A charging capacitor draws a conduction current of 1 A through its wires. What is the displacement current between its plates?
Show the worked solution
- The Ampere-Maxwell law keeps the current continuous around any loop.
- What the wire delivers, the changing electric flux between the plates carries on.
Answer: 1 A - the displacement current exactly equals the conduction current.
Check: That equality is why the magnetic field around the gap matches the field around the wire.
Watch for this: Displacement current is not a flow of charge - it is a changing electric field acting as a magnetic source.
Now try it yourself
The same capacitor at a moment when the wire carries 0.4 A. Displacement current?
Check your answer
0.4 A.
The two are equal at every instant of the charging.
The speed from the constants
Choose the method: c = 1/sqrt(mu0 epsilon0).
EZT practice question
Using mu0 = 4 pi x 10^-7 and epsilon0 = 8.85 x 10^-12 (both SI), estimate the speed of electromagnetic waves in vacuum.
Show the worked solution
- mu0 x epsilon0 = 1.257 x 10^-6 x 8.85 x 10^-12 = 1.11 x 10^-17.
- sqrt of that is 3.33 x 10^-9.
- c = 1 / 3.33 x 10^-9.
Answer: c = 3 x 10^8 m/s (approximately).
Check: Maxwell's theory predicted this value from purely electrical measurements - and it matched the measured speed of light, which is how light was recognised as an EM wave.
Watch for this: Take the square root of the PRODUCT, then invert - inverting first scrambles the units.
Now try it yourself
In a medium with mu = mu0 and epsilon = 4 epsilon0, wave speed?
Check your answer
1.5 x 10^8 m/s.
Four times the permittivity doubles the denominator, halving the speed.
Order the spectrum
Choose the method: Long wavelength to short: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
EZT practice question
Arrange microwaves, gamma rays and radio waves in order of increasing frequency.
Show the worked solution
- Frequency rises as wavelength falls.
- Radio waves are longest, gamma rays shortest.
Answer: Radio waves, then microwaves, then gamma rays.
Check: Each step up in frequency is a step up in photon energy - gamma rays are the most energetic of the three.
Watch for this: Do not confuse the two orderings - wavelength increases exactly opposite to frequency.
Now try it yourself
Where does visible light sit relative to infrared and ultraviolet?
Check your answer
Between them - higher frequency than infrared, lower than ultraviolet.
The visible slice splits the warm infrared below from the burning ultraviolet above.
Try a mixed set
Choose a method or explanation before opening each answer.
1. E and B amplitudes?
Show answer and reason
E0 / B0 = c.
B0 = E0 / 3 x 10^8 in vacuum.
2. Wavelength from frequency?
Show answer and reason
lambda = c / f.
Their product is the wave speed.
3. Displacement current?
Show answer and reason
i_d = epsilon0 d(phi_E)/dt.
A changing electric flux makes a magnetic field.
4. Spectrum order?
Show answer and reason
Radio, micro, infrared, visible, UV, X-ray, gamma.
Frequency and energy rise along the list.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- A wave has E0 = 120 V/m. Find B0.
- A 30 MHz radio signal. Find its wavelength.
- A 10 GHz radar. Find its wavelength.
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Questions about this practice page
- What is displacement current?
- Maxwell's addition to Ampere's law: a changing electric flux, i_d = epsilon0 d(phi_E)/dt, produces a magnetic field just as a conduction current does. It explains the magnetic field between a charging capacitor's plates, where no charge actually flows.
- Are the E and B fields of a light wave out of phase?
- No. In a plane electromagnetic wave the electric and magnetic fields oscillate IN phase - they peak together and vanish together - while pointing perpendicular to each other and to the direction of travel.
- How is the electromagnetic spectrum ordered?
- From long wavelength and low frequency to short and high: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Photon energy climbs steadily along the same direction.
- What are the main uses of each band?
- Radio for broadcasting, microwaves for radar and ovens, infrared for heaters and night vision, visible for sight, ultraviolet for sterilisation, X-rays for medical imaging, and gamma rays for cancer treatment - sections 8.4.1 to 8.4.7 take them one by one.
- Are these the NCERT exercise questions for Electromagnetic Waves (Class 12)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.