NCERT Exemplar solutions for Physics [English] Class 12 chapter 8 - Electromagnetic Waves [Latest edition]

One requires 11eV of energy to dissociate a carbon monoxide molecule into carbon and oxygen atoms. The minimum frequency of the appropriate electromagnetic radiation to achieve the dissociation lies in ______.

A linearly polarized electromagnetic wave given as E = E_oî cos (kz – ωt) is incident normally on a perfectly reflecting infinite wall at z = a. Assuming that the material of the wall is optically inactive, the reflected wave will be given as ______.

Light with an energy flux of 20 W/cm² falls on a non-reflecting surface at normal incidence. If the surface has an area of 30 cm² the total momentum delivered (for complete absorption) during 30 minutes is ______.

The electric field intensity produced by the radiations coming from 100 W bulb at a 3 m distance is E. The electric field intensity produced by the radiations coming from 50 W bulb at the same distance is ______.

If `vecE` and `vecB` represent electric and magnetic field vectors of the electromagnetic wave, the direction of propagation of the electromagnetic wave is along ______.

The ratio of contributions made by the electric field and magnetic field components to the intensity of an EM wave is ______.

An EM wave radiates outwards from a dipole antenna, with E₀ as the amplitude of its electric field vector. The electric field E₀ which transports significant energy from the source falls off as ______.

An electromagnetic wave travels in vacuum along z direction: `E = ( E_1hati + E_2hatj ) cos (kz - ωt)`. Choose the correct options from the following:

1. The associated magnetic field is given as `B = 1/c(E_1hati - E_2hatj) cos (kz - ωt)`.
2. The associated magnetic field is given as `B = 1/c(E_1hati - E_2hatj) sin (kz - ωt)`.
3. The given electromagnetic field is circularly polarised.
4. The given electromagnetic wave is plane polarised.

An electromagnetic wave travelling along z-axis is given as: E = E₀ cos (kz – ωt.). Choose the correct options from the following;

1. The associated magnetic field is given as `B = 1/c hatk xx E = 1/ω (hatk xx E)`.
2. The electromagnetic field can be written in terms of the associated magnetic field as `E = c(B xx hatk)`.
3. `hatk.E = 0, hatk.B` = 0.
4. `hatk xx E = 0, hatk xx B` = 0.

A plane electromagnetic wave propagating along x direction can have the following pairs of E and B.

1. E_x, B_y.
2. E_y, B_z.
3. B_x, E_y.
4. E_x, B_y.

A charged particle oscillates about its mean equilibrium position with a frequency of 10⁹ Hz. The electromagnetic waves produced ______.

1. will have frequency of 10⁹ Hz.
2. will have frequency of 2 × 10⁹ Hz.
3. will have a wavelength of 0.3 m.
4. fall in the region of radiowaves.

The source of electromagnetic waves can be a charge ______.

1. moving with a constant velocity.
2. moving in a circular orbit.
3. at rest.
4. falling in an electric field.

An EM wave of intensity I falls on a surface kept in vacuum and exerts radiation pressure p on it. Which of the following are true?

1. Radiation pressure is `I/c` if the wave is totally absorbed.
2. Radiation pressure is `I/c` if the wave is totally reflected.
3. Radiation pressure is `(2I)/c` if the wave is totally reflected.
4. Radiation pressure is in the range `I/c < p < (2I)/c` for real surfaces.

Why is the orientation of the portable radio with respect to broadcasting station important?

Why does microwave oven heats up a food item containing water molecules most efficiently?

The charge on a parallel plate capacitor varies as q = q₀ cos 2πνt. The plates are very large and close together (area = A, separation = d). Neglecting the edge effects, find the displacement current through the capacitor?

A variable frequency a.c source is connected to a capacitor. How will the displacement current change with decrease in frequency?

The magnetic field of a beam emerging from a filter facing a floodlight is given by B₀ = 12 × 10^–8 sin (1.20 × 10⁷z – 3.60 × 10¹⁵t) T. What is the average intensity of the beam?

Poynting vectors S is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the direction of wave propagation. Mathematically, it is given by `S = 1/mu_0 E xx B`. Show the nature of S vs t graph.

Professor C.V Raman surprised his students by suspending freely a tiny light ball in a transparent vacuum chamber by shining a laser beam on it. Which property of EM waves was he exhibiting? Give one more example of this property.

Show that the magnetic field B at a point in between the plates of a parallel-plate capacitor during charging is `(ε_0mu_r)/2 (dE)/(dt)` (symbols having usual meaning).

Electromagnetic waves with wavelength

1. λ₁ is used in satellite communication.
2. λ₂ is used to kill germs in water purifies.
3. λ₃ is used to detect leakage of oil in underground pipelines.
4. λ₄ is used to improve visibility in runways during fog and mist conditions.

1. Identify and name the part of electromagnetic spectrum to which these radiations belong.
2. Arrange these wavelengths in ascending order of their magnitude.
3. Write one more application of each.

Show that average value of radiant flux density ‘S’ over a single period ‘T’ is given by S = `1/(2cmu_0) E_0^2`.

You are given a 2 µF parallel plate capacitor. How would you establish an instantaneous displacement current of 1 mA in the space between its plates?

Show that the radiation pressure exerted by an EM wave of intensity I on a surface kept in vacuum is I/c.

What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a room, its intensity essentially remains constant. What geometrical characteristic of LASER beam is responsible for the constant intensity which is missing in the case of light from the bulb?

Even though an electric field E exerts a force qE on a charged particle yet the electric field of an EM wave does not contribute to the radiation pressure (but transfers energy). Explain.

An infinitely long thin wire carrying a uniform linear static charge density λ is placed along the z-axis (figure). The wire is set into motion along its length with a uniform velocity `v = vhatk_z`. Calculate the poynting vector `S = 1/mu_0 (E xx B)`.

Sea water at frequency ν = 4 × 10⁸ Hz has permittivity ε ≈ 80 εo, permeability µ ≈ µo and resistivity ρ = 0.25 Ω–m. Imagine a parallel plate capacitor immersed in seawater and driven by an alternating voltage source V(t) = V_o sin (2πνt). What fraction of the conduction current density is the displacement current density?

A long straight cable of length `l` is placed symmetrically along z-axis and has radius a(<< l). The cable consists of a thin wire and a co-axial conducting tube. An alternating current I(t) = I₀ sin (2πνt) flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is E(s,t) = µ₀I₀ν cos (2πνt) In `(s/a)hatk`.

1. Calculate the displacement current density inside the cable.
2. Integrate the displacement current density across the cross-section of the cable to find the total displacement current I^d.
3. Compare the conduction current I0 with the displacement current `I_0^d`.

A plane EM wave travelling in vacuum along z direction is given by `E = E_0 sin(kz - ωt)hati` and `B = B_0 sin(kz - ωt)hatj` 

1. Evaluate `oint E.dl` over the rectangular loop 1234 shown in figure.
2. Evaluate `int B.ds` over the surface bounded by loop 1234.
3. Use equation `oint E.dl = (-dphi_B)/(dt)` to prove `E_0/B_0` = c.
4. By using similar process and the equation `ointB.dl = mu_0I + ε_0 (dphi_E)/(dt)`, prove that c = `1/sqrt(mu_0ε_0)`

A plane EM wave travelling along z direction is described by `E = E_0 sin (kz - ωt)hati` and `B = B_0 sin (kz - ωt)hatj`. show that 

1. The average energy density of the wave is given by `u_(av) = 1/4 ε_0E_0^2 + 1/4 B_0^2/mu_0`.
2. The time averaged intensity of the wave is given by `I_(av) = 1/2 cε_0 E_0^2`.