Thirty multiple choice questions. Two previous year questions sit in Section D — the X-ray frequency comparison from 2025 and the displacement current calculation from 2021, both worked in full.
30questions
35 minsuggested time
6verified PYQs
MCQformat throughout
Score0 correct · 0 of 30 attempted
Before you begin
Formulas you will need
Key formulas
c = 1 ∕ √(μ0ε0) = 3 × 108 m s−1 · c = fλ · E0 ∕ B0 = c
Displacement current: Id = ε0 dΦE ∕ dt · Speed in a medium: v = c ∕ n
Momentum delivered: p = U ∕ c · Intensity ∝ E02
Spectrum by rising frequency: radio → microwave → infrared → visible → ultraviolet → X-ray → gamma
How to use this worksheet. Learn the spectrum order once — radio, microwave, infrared, visible, ultraviolet, X-ray, gamma — and every comparison question answers itself. For displacement current, find the capacitance first, then the charge, then divide by the time.
Section A · Level 1
Nature of electromagnetic waves and the spectrum
Ten questions. None should take more than twenty seconds.
Q1
The speed of electromagnetic waves in vacuum is closest to:
All electromagnetic waves travel at 3 × 108 m/s in vacuum, whatever their frequency.
Q2
The speed of light in vacuum is given by:
Maxwell showed that c = 1 ∕ √(μ0ε0). Substituting the measured constants gives almost exactly the measured speed of light, which is how light was identified as an electromagnetic wave.
Q3
Electromagnetic waves are:
The electric and magnetic fields both oscillate perpendicular to the direction of travel, so the wave is transverse. That is why light can be polarised.
Q4
In an electromagnetic wave, the electric and magnetic field vectors are:
E, B and the direction of propagation form a mutually perpendicular set, with the wave travelling along the direction of E × B.
Q5
Electromagnetic waves:
Because the changing electric and magnetic fields sustain one another, the wave propagates through vacuum with no medium at all.
Q6
The concept of displacement current was introduced by:
Maxwell added the displacement current term to Ampere's law so that it would hold in the gap of a charging capacitor. That correction predicted electromagnetic waves.
Q7
Which of these has the longest wavelength?
Radio waves sit at the low-frequency end of the spectrum, so they have the longest wavelengths — metres to kilometres.
Q8
The approximate wavelength range of visible light is:
Visible light runs from about 400 nm at the violet end to about 700 nm at the red end.
Q9
Which of the following carries photons of the highest energy?
Photon energy is proportional to frequency, and gamma rays sit at the top of the spectrum, so they carry the most energetic photons.
Q10
Electromagnetic waves carry:
An electromagnetic wave transports both energy and momentum, which is why radiation pressure exists and why solar sails work.
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Section B · Level 2
Wavelength, frequency and uses
Nine questions. Use c = fλ and know what each band is used for.
Q11
An electromagnetic wave in vacuum has a wavelength of 3 m. Its frequency is:
f = c ∕ λ = (3 × 108) ∕ 3 = 108 Hz, which is 100 MHz — the FM radio band.
Q12
A radio station broadcasts at 100 MHz. The wavelength of its signal is:
λ = c ∕ f = (3 × 108) ∕ (100 × 106) = 3 m.
Q13
The ratio of the amplitudes of the electric and magnetic fields in an electromagnetic wave equals:
E0 ∕ B0 = c. Because c is large, the numerical value of B is always far smaller than that of E in SI units, which is why the magnetic part is easy to overlook.
Q14
In an electromagnetic wave, the average energy density of the electric field compared with that of the magnetic field is:
The two contributions are exactly equal, each carrying half of the total energy density of the wave.
Q15
Which region of the spectrum is used in radar and in microwave ovens?
Microwaves are used for radar because they reflect well off aircraft and can be formed into narrow beams, and for ovens because water molecules absorb them strongly.
Q16
Infrared radiation is commonly used in:
Remote controls emit short infrared pulses. Infrared is also used in thermal imaging, since warm objects radiate strongly in that band.
Q17
X-rays are most commonly used for:
X-rays pass through soft tissue but are absorbed by bone, which is what produces the contrast in a radiograph.
Q18
The ultraviolet radiation reaching the Earth is largely absorbed by:
Ozone in the stratosphere absorbs most of the harmful ultraviolet, which is why depletion of that layer is a serious concern.
Q19
Which of these is chiefly responsible for the greenhouse effect in the atmosphere?
Sunlight arrives mostly as visible light and warms the surface, which re-radiates in the infrared. Greenhouse gases absorb that infrared and trap the energy.
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Section C · Level 3
Displacement current, propagation and energy
Nine questions. Each needs a formula plus a piece of reasoning.
Q20
The displacement current between the plates of a charging capacitor is given by:
Maxwell defined the displacement current as ε0 times the rate of change of electric flux. In the gap of a capacitor it exactly equals the conduction current in the wires.
Q21
The displacement current in the gap of a charging capacitor is:
This equality is precisely what makes the Ampere-Maxwell law consistent, whichever surface you choose to apply it to.
Q22
The direction of propagation of an electromagnetic wave is given by the direction of:
The Poynting vector E × B points along the direction of energy flow, which is the direction the wave travels. Reversing the order would point backwards.
Q23
The speed of an electromagnetic wave in a medium of refractive index n is:
Light slows in a medium to c ∕ n. The frequency is unchanged, so it is the wavelength that shortens.
Q24
When an electromagnetic wave enters a denser medium, its frequency:
Frequency is fixed by the source, so it does not change on entering a new medium. Speed and wavelength both fall in the same proportion.
Q25
The intensity of an electromagnetic wave is proportional to:
Intensity depends on the square of the field amplitude, so doubling the amplitude quadruples the energy delivered per second.
Q26
The momentum delivered by an electromagnetic wave that transfers energy U to a fully absorbing surface is:
For complete absorption the momentum transferred is U ∕ c. If the surface reflects the wave instead, the momentum transfer doubles.
Q27
Gamma rays are produced by:
Gamma rays originate in nuclear transitions and in radioactive decay, which is why their photon energies are so much larger than those from atomic processes.
Q28
A parallel plate capacitor of plate area 25 cm² and plate separation 5 mm is charged to 100 V in a time of 1 µs. The average displacement current is closest to:
C = ε0A ∕ d = (8.854 × 10−12 × 25 × 10−4) ∕ (5 × 10−3) = 4.43 × 10−12 F. Then Q = CV = 4.43 × 10−10 C, and dividing by 10−6 s gives about 0.44 mA. This is the same set-up as one of the previous year questions.
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Section D · Previous year questions
Straight from the AAI ATC papers
Six questions, exactly as they appeared. Four come from the 2023 papers, recovered by optical character recognition of the scanned answer sheets and independently re-solved.
Q29PYQ 2023 · Morning
Let λ₁, λ₂, λ₃ and λ₄ be the wavelengths of microwaves, gamma rays, ultraviolet rays and infrared rays respectively. Then:
Order the four by wavelength, longest first: microwaves, then infrared, then ultraviolet, then gamma rays. In the labelling given that is λ₁ > λ₄ > λ₃ > λ₂. Wavelength runs the opposite way to frequency, so write the spectrum out in one order and read it backwards rather than trying to hold both in your head.
Q30PYQ 2023 · Morning
When sunlight passes through the earth's atmosphere it is scattered by atmospheric particles. For light of wavelength λ, the amount of scattering is proportional to:
This is Rayleigh scattering, which goes as one over the fourth power of the wavelength. Short wavelengths scatter far more strongly, which is why the sky is blue and why the sun looks red at sunset when the light has travelled a long path through the atmosphere.
Q31PYQ 2023 · Evening
Infrared waves are produced by:
Infrared radiation comes from the thermal vibration of atoms and molecules, so any warm object emits it. Accelerating charges in a wire produce radio waves, and X-rays come from vacuum tubes — each band of the spectrum has its own characteristic source.
Q32PYQ 2023 · Evening
A plane electromagnetic wave of frequency 10 MHz travels in free space along the y-direction. At a particular point in space and time, E = 9.9 V/m. The magnitude of B at this point is:
In an electromagnetic wave the two field amplitudes are linked by E ∕ B = c, so B = E ∕ c = 9.9 ∕ (3 × 108) = 3.3 × 10−8 T. The frequency and the direction of travel are not needed at all. Every wrong option has the right figure of 3.3 and the wrong power of ten, so the exponent is the entire question.
Q33PYQ 2025 · Shift 2
The frequency of X-rays is less than the frequency of:
Running up the spectrum by frequency: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Only gamma rays sit above X-rays, so all three other options have lower frequencies. Learning the order once answers every spectrum question in the paper.
Q34PYQ 2021 · Shift 3
Assume a parallel plate capacitor which is maintained at a potential of 100 V. If the partition distance between the plates of the capacitor and the area of the plates are 5 mm and 25 cm² respectively, compute the displacement current for a time of 1 µs.
First find the capacitance: C = ε0A ∕ d = (8.854 × 10−12 × 25 × 10−4) ∕ (5 × 10−3) = 4.43 × 10−12 F. The charge is Q = CV = 4.43 × 10−10 C, and the displacement current is the rate of change of that charge, Q ∕ t = 4.43 × 10−10 ∕ 10−6 = 4.43 × 10−4 A, or about 0.44 mA. Converting cm² to m² is where this one usually goes wrong.
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Answer key
Answers
Check only after you have attempted every question. Tap any question above to see the full worked solution.
All thirty questions with the formula sheet printed on the front page and ruled working space for your circuit reductions. Print it, solve it, keep it.
Seven questions from one chapter in a single year.
Live classes cover the full Class 11 and 12 physics and maths syllabus for AAI ATC, taught from the real question papers with the method for each question type drilled until it is automatic.