This chapter is crucial for board and competitive exams because it links Maxwell’s equations to observable wave properties like reflection/refraction, energy and momentum transport (Poynting vector), wave polarization, and dispersion effects in media (including plasmas). Strong command of these ideas helps you solve numerical and conceptual questions efficiently and accurately.
20
Minutes
15
Questions
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Marking
Q1. A plane electromagnetic wave propagates in vacuum. A field-measuring instrument records the rms value of the electric field as . What is the time-averaged intensity (time-average of the magnitude of the Poynting vector) of the wave? Use and .
Q2. A monochromatic plane EM wave of angular frequency propagates in a non-magnetic dielectric (permittivity , permeability ) with small conductivity . For a good dielectric () the attenuation constant is approximated by . Show that the amplitude after one wavelength in the medium is reduced approximately by . If , what is the numerical value of the amplitude ratio after one wavelength?
Q3. In a dispersive medium the refractive index depends on angular frequency as with constants and . For frequencies satisfying , the phase velocity is and the group velocity is . Which of the following correctly states the relation between and for those frequencies?
Cannot determine without numerical values of and
Q4. Two identical monochromatic plane electromagnetic waves of angular frequency and electric-field amplitude travel in opposite directions in vacuum and form a standing wave. Which statement correctly describes the time-averaged energy densities at a point which is an electric-field antinode (where )?
The time-averaged electric energy density is and the time-averaged magnetic energy density equals .
The time-averaged total energy density varies with as .
The time-averaged total energy density is zero everywhere.
At an electric-field antinode the time-averaged electric energy density equals while the time-averaged magnetic energy density is zero; moreover the time-averaged total energy density is uniform in space with value .
Q5. Assertion (A): For an electromagnetic wave with angular frequency propagating in a collisionless plasma with plasma frequency and , the phase velocity is .
Reason (R): This superluminal phase velocity does not violate special relativity because information and energy propagate at the group velocity , and in fact .
Which option is correct?
Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true, R is false.
A is false, R is true.
Q6. A plane electromagnetic wave in vacuum is described by the electric field with amplitude . Using and , the time-averaged intensity is . Its numerical value (in ) is:
Q7. A plane electromagnetic wave in air () is normally incident on a non-magnetic dielectric () whose relative permittivity is . Neglect absorption and multiple internal reflections. The fraction of incident intensity transmitted across the first surface into the dielectric is:
Q8. A plane electromagnetic wave of amplitude in vacuum is normally incident on a non-magnetic dielectric () with relative permittivity . Neglect reflections beyond the first interface. If the transmitted electric amplitude is , the time-averaged electromagnetic energy density in the dielectric is and in vacuum . The ratio equals:
Q9. Consider a parallel-plate capacitor being charged by a battery. Let the plates be large circular disks of radius separated by distance . Assertion A: "During charging, the electromagnetic energy delivered by the battery flows into the capacitor through the region between the plates as a Poynting flux (fields carry energy into the gap)." Reason R: "The energy density stored between the plates at any instant is , where is the electric field between the plates." Choose the correct option:
Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Q10. A monochromatic plane electromagnetic wave of intensity is incident at angle on a flat surface with reflectivity (fraction of incident power reflected; remainder absorbed). The radiation pressure normal to the surface is . Using , the numerical value of is approximately:
Q11. A plane electromagnetic wave in vacuum has electric field amplitude . Calculate the time‑averaged intensity (time‑average magnitude of the Poynting vector) of the wave. Use and .
Q12. A plane electromagnetic wave in vacuum () is normally incident on a non‑magnetic dielectric with relative permittivity . Neglect absorption. Using the characteristic impedance , what fraction of the incident intensity is transmitted into the dielectric?
Q13. For a conductor with conductivity , an electromagnetic wave of frequency has skin depth where . If a plane wave at this frequency traverses a slab whose thickness equals one skin depth (), what fraction of the incident intensity emerges from the far side (time‑averaged transmitted intensity divided by incident intensity)?
Q14. Assertion (A): For an electromagnetic wave in a material with refractive index the group velocity and phase velocity are related by .
Reason (R): Since , one gets and hence .
Both A and R are true but R is not a correct explanation of A.
A is true but R is false.
Both A and R are true and R is a correct explanation of A.
A is false but R is true.
Q15. A plane electromagnetic wave of intensity is incident on a perfectly reflecting flat surface at angle measured from the surface normal. What is the radiation pressure (force per unit area normal to the surface) on the surface? Take .