Q: Dimensions of 1/(μ0ε0) is:

(c) L2/T2 The speed of light, C=H01 The dimensions of H01 are of velocity, ie. L/T . Therefore, z1μ01 will have dimensions L2/T2

Question 1

In a microwave oven, the food is kept in a plastic container and the microwaves is directed towards the food. The food is cooked without melting or igniting the plastic container. Explain.

Accepted Answer

The natural frequency of water matches the frequency of microwave. This is the reason that food containing water gets cooked. The natural frequency of the plastic container does not match the frequency of microwave. So, the plastic container is not damaged.

Question 2

A metal rod is placed along the axis of a solenoid carrying a high-frequency alternating current. It is found that the rod gets heated. Explain why the rod gets heated.

Accepted Answer

The magnetic field along the axis of a solenoid carrying a high-frequency alternating current changes continuously. Due to the change in the magnetic field, e.m.f (or eddy current) is induced in the metal rod. There will be flow of charge due to the induced e.m.f. The direction of the induced e.m.f changes very frequently due to the high-frequency alternating current in the solenoid. Thus, the rod gets heated up due to the flow of charge in it.

Question 3

Can an electromagnetic wave be deflected by an electric field? By a magnetic field ?

Accepted Answer

No, an electromagnetic wave cannot be deflected by an electric field or a magnetic field. This is because according to Maxwell's theory, an electromagnetic wave does not interact with the static electric field and magnetic field. Even if we consider the particle nature of the wave, the photon is electrically neutral. So, it is not affected by the static magnetic and electric fields.

Question 4

A wire carries an alternating current i =i0​  sin ωt. Is there an electric field in the vicinity of the wire?

Accepted Answer

When an alternating current passes through a conductor, the changing magnetic field create a changing electric field outside it. An electromagnetic field is radiated from the surface of the conductor. There is a time-varying electric field outside the conductor. Hence, there is a time-varying electric field in the vicinity of the wire.

Question 5

A capacitor is connected to an alternating-current source. Is there a magnetic field between the plates?

Accepted Answer

When an alternating-current source is connected to a capacitor, the electric field between the plates of the capacitor keeps on changing with the applied voltage. Due to the changing electric field, a magnetic field exists in between the plates of the capacitor.

Question 6

Can an electromagnetic wave be polarised?

Accepted Answer

An electromagnetic wave is a transverse wave; thus, it can be polarised. An unpolarised wave consists of many independent waves, whose planes of vibrations of electric and magnetic fields are randomly oriented. They are polarised by restricting the vibrations of the electric field vector or magnetic field vector in one direction only.

Question 7

A plane electromagnetic wave is passing through a region. Consider (a) electric field (b) magnetic field (c) electrical energy in a small volume and (d) magnetic energy in a small volume. Construct the pairs of the quantities that oscillate with equal frequencies.

Accepted Answer

Let the electromagnetic wave be propagating in the z-direction. The vibrations of the electric and magnetic fields are given by:​Ex​=E0​sin(kz−ωt)By​=BD​sin(kz−ωt)​ Let the volume of the region be V .The angular frequency of the vibrations of the electric and magnetic fields are same and are equal to w. Therefore, their frequency, f=2xω​ , is same.The electrical energy in the region,UE​=(21​∈0E2)×V It can be written as: UE​=(21​∈θ(E02​sin2(kz−ωt))×V  UE​=(21​ϵ0​E02​×2(1−cos2(kz−ωt))​)×V  UE​=(41​∈0​E02​×(1−cos2(kz−ωt)))×V The magnetic energy in the region,UB​=(2μ0​JE​)×V UB​=(2μˉ​0​B02​sin2(kz−ωt)​)×V ⇒UB​=(4p4​​B0I​(1−∞)(2kz−2,t))​)×V The angular frequency of the electric and magnetic energies is same and is equal to 2ω . Therefore, their frequency,f′=2π2​=2f ; will be same.Thus, the electric and magnetic fields have same frequencies and the electrical and magnetic energies will have same frequencies.

Question 8

A magnetic field can be produced by:

Accepted Answer

(d) Both of them  Both of themAccording to Ampere-Maxwell's Law, a magnetic field is produced due to the conduction current in a conductor and the displacement current. The conduction current is actually the motion of the charge. The displacement current is due to the changing electric field. The displacement current is given by id​=ε0dldwg​​(∵ϕE​ is the electric flux). Thus, the magnetic field is produced by the  moving charge as well as the changing electric field.

Question 9

A compass needle is placed in the gap of a parallel plate capacitor. The capacitor is connected to a battery through a resistance. The compass needle:

Accepted Answer

(d) deflects and gradually comes to the original position in a time that is large compared to the time constant,The compass needle deflects due to the presence of the magnetic field. Inside the capacitor, a magnetic field is produced when there is a changing electric field inside it. As the cepacitor is connected across the battery, the charge on its plates at a certain time t is given by.Q=CV(1−e−5/70)  whereQ= charge developed on the plates of the capacitorR= resistance of the resistor connected in series with the capacitorC= capacitance of the capacitorV= potential difference of the batteryThe time constant of the capacitor is given, τ=RC The capacitor keeps on charging up to the time τ . The development of charge on the plates will be gradual after t=RC . The change in electric field will be up to the time the charge is developing on the plates of the capacitor. Thus, the compass needle deflects and gradually comes to the original position] in a time that is large compared to the time constant.

Question 10

Dimensions of 1/(μ0​ε0​)  is:

Accepted Answer

(c) L2/T2 The speed of light, C=H0​​1​ The dimensions of H0​​1​  are of velocity, ie. L/T . Therefore, z1​μ0​1​  will have dimensions L2/T2

Question 11

Electromagnetic waves are produced by:

Accepted Answer

an accelerating chargeA static charge produces an electrostatic field. A moving charge produces a magnetic field. Electromagnetic waves are produced by an accelerating charge.

Question 12

An electromagnetic wave going through vacuum is described by E=E0​sin(kx−ωt);B=B0​sin(kx−ωt). Then:

Accepted Answer

(a) E0​k=B0​ω The relation between E0​  and B0​  is given by B0​E0​​=c…(1) Here, c= speed of the electromagnetic waveThe relation between ω  (the angular frequency) and k (wave number)kˉω​=c…(2) Therefore, from (1) and (2), we get.​B0​R4​​=kω​=c⇒E0​k=B0​ω​

Question 13

An electric field E  and a magnetic field B  exist in a region. The fields are not perpendicular to each other.

Accepted Answer

An electromagnetic wave may be passing through the region.For an electromagnetic wave,electric field ,magnetic field and direction of propagation are mutually perpendicular to each other.We can have a region in which electric and magnetic fields are applied at an angle with each other.In transmission lines Different modes exist. In transverse electric (TE) mode-no electric field exist in the direction of propagation. These are sometimes called H modes because there is only a magnetic field along the direction of propagation (H is the conventional symbol for magnetic field).

Question 14

Consider the following two statements regarding a linearly polarised, plane electromagnetic wave :(A) The electric field and the magnetic field have equal average values.(B) The electric energy and the magnetic energy have equal average values.

Accepted Answer

(a) Both A  and B  are true.For a linearly polarised, plane electromagnetic wave​E=E0​sinω(t−z/c)B=B0​sinω(t−x/c)​ The average value of either Eor B  over a cycle is zero ( average of sin(θ)  over a cycle is zero). Also the electric energy density (uk​)  and magnetic energy density (uB​)  are equal.uE=21​∈0E2=2μ1​B2​=uIB Energy can be found out by integrating energy density over the entire volume of full space. As the energy of the electromagnetic wave is equally shared between electric and magnetic field so their average values will also be equal.

Question 15

A free electron is placed in the path of a plane electromagnetic wave. The electron will start moving:

Accepted Answer

(a) along the electric fieldAs the electron is at rest initially, only the electric field will exert force on it. There will be no magnetic force on the electron in the stating. Hence, the electron will start moving along the electric field.

Question 16

A plane electromagnetic wave is incident on a material surface. The wave delivers momentum p and energy E.

Accepted Answer

(c) ρ=0,E=0 When an electromagnetic wave strikes a material surface, it transports the momentum, as well as the energy, to the surface. The striking electromagnetic wave exerts pressure on the surface. The total energy transferred to the surface by the electromagnetic wave is given by E=pc . Therefore, p=0,E=0.

Question 17

An electromagnetic wave going through vacuum is described by E=E0​sin(kx−ωt) .Which of the following is/are independent of the wavelength?

Accepted Answer

The given quantities can be expressed as:k is given byk=λ2π​ ω  is given by​ω=2πνc=νλ⇒ω=2πλc​​ k′ω  is given by ωk​=2πc/λ2π/λ​=c1​ kω is given byk×ω=λ2π​×λ2πc​=λ24π2c​ Thus, k/ω  is independent of the wavelength.

Question 18

Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor:

Accepted Answer

(a) increases(b) decreasesDisplacement current inside a capacitor,id​=ε0​aldϕk​​ , whereϕE​  is the electric flux inside the capacitor.Up to the time the electric flux changes, there will be a displacement current. This is possible when the charge on a capacitor changes. Therefore, the displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor or electric field increases or decreases inside the capacitor.

Question 19

Speed of electromagnetic waves is the same:

Accepted Answer

(c) for all intensitiesFor any given medium, the speed (c) of an electromagnetic wave is given byc=vλ,  wherev= frequency of the electromagnetic waveλ=  wavelength of the electromagnetic waveAs the frequency and wavelength are changed, the speed of the electromagnetic wave changes. So, the speed of an electromagnetic wave is not same for all wavelengths and all frequencies in any medium. The velocity of an electromagnetic wave changes with change in medium. Also, the speed of an electromagnetic wave is same for all the intensities in any medium.

Question 20

Which of the following have zero average value in a plane electromagnetic wave?

Accepted Answer

(a) Electric field(b) Magnetic fieldIn a plane electromagnetic wave, the electric and the magnetic fields oscillate sinusoidally. For an electromagnetic wave propagating in the z-direction, the electric and magnetic fields are given by.Ex​=E0​sin(kz−ωt) By​=B0​sin(kz−ωt) These are sinusoidal functions. Therefore, for a fixed value of z, the average value of the electric and magnetic fields are zero.

Chapter 18 : Electromagnetic Waves