Q: The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is:

The intensity of an electromagnetic wave is given by:\$I=U_{av}c\$here, \$U_{av}\$ is the average energy and \$c\$ is the speed of light.The average energy in terms of the electric field is written as:\$U_{av}=\dfrac 12\varepsilon_oE_o^2\$Average energy in terms of magnetic field:\$U_{av}=\dfrac 12\dfrac{B_o^2}{\mu_o}\$We know that, \$E_o=cB_o\$ and \$c=\dfrac{1}{\sqrt{\mu_o\varepsilon_o}}\$\$\therefore U_{av\ (electric\ field)}=\dfrac 12\varepsilon_o\times\dfrac{1}{\mu_o\varepsilon_o}B_o^2\$\$\Rightarrow\dfrac 12\dfrac{B_o^2}{\mu_o}\$Since the energy due to electric and magnetic field is same. so, both will have the same contribution to the intensity.

Q: The rms value of the electric field of the light coming from sun is 720 N \$C^{-1}\$. The average total energy density of the electromagnetic wave is

Given: The RMS value of the electric field of light is \$720\ N/C\$.Energy density of electromagnetic wave is given by:\$E=\epsilon_0 E_{rms}^2\$ \$=8.85\times 10^{-12}\times (720)^2\$\$E\approx 4.58\times 10^{-6}J/m^3\$Option \$(B)\$ is corret.

Q: Magnetic field in a plane electromagnetic wave is given by \$ \overrightarrow{B} = B_0 sin (kx + \omega t) \hat{j} T \$Expression for corresponding electric field will be :Where c is speed of light.

\$\dfrac{\overrightarrow{E}}{\overrightarrow{B}}=C\$\$\overrightarrow{B} = B_0\sin(kx + \omega t)\$\$\overrightarrow {E} = B_0C\sin(kx+\omega t)\hat k\$ \$V/m\$

Q: The amplitude of the magnetic field of a harmonic electromagnetic wave in vacuum is \${B}_{0}\$ = 510 nT. The amplitude of the electric field part of the wave is

Given,\$B_0=510nT\$\$c=3\times 10^8m/s\$The magnitude of electric field is given by\$E_0=B_0 c\$\$E_0=510\times 10^{-9}\times 3\times 10^8\$\$E_0=153NC^{-1}\$The correct option is D.

Q: A parallel plate capacitor with circular plates of radius \$R\$ is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between \$\cfrac{R}{2}\$ and \$R\$ is given by

Displacement current is given by \$ I={{\varepsilon }_{0}}\dfrac{d{{\phi }_{e}}}{dt} \$ \$ =\,{{\varepsilon }_{0}}A\dfrac{dE}{dt}\,\,\,\,(\because \,\phi =A.E) \$ \$ =A\dfrac{d}{dt}\left(\dfrac{q}{{{A}^{'}}}\right) \$ \$ =\dfrac{A}{{{A}^{'}}}i\,\,(\because \dfrac{dq}{dt}=i) \$ \$ =\dfrac{\pi {{\left(\dfrac{R}{2}\right)}^{2}}}{\pi {{R}^{2}}} \$ \$ =\dfrac{1}{4}i \$

Q: Maxwell's modified form of Ampere's circuital law is

\$Answer:-\$ DTreating all charges on the same footing (disregarding whether they are bound or free charges), the generalized Ampère's equation, also called the Maxwell–Ampère equation, is in integral form.

Question 1

List the properties of electromagnetic waves.

Accepted Answer

Electromagnetic waves are composed oscillating electric and magnetic field at right angles to each other.PropertiesElectromagnetic waves are propagated by oscillating electric fields and magnetic field oscillation at right angles to each other.These waves travel with speed $3\times { 10 }^{ 8 }m{ s }^{ -1 }$ in vacuum.They are not deflected by electric or magnetic field.They can show interference or diffraction.They are transverse waves.May be polarized.Need no medium of propagation.wavelength and frequency related as $c=v\lambda  $.

Question 2

What is displacement current? Obtain an expression of displacement current for a charged capacitor. Write Ampere-Maxwell's law.

Accepted Answer

When a capacitor is charging (or discharging), current flows in the circuit. However, there is no actual charge transfer in the insulated region between capacitor which is contradictory to the flow of current. Hence, displacement current is the current in the insulated region due to the changing electric flux.For a charged capacitor, electric field between the plates is given by:$E = \cfrac{Q}{\varepsilon_o A}$$Q = \varepsilon_o \phi_E$Displacement current is given by:$i_d = \cfrac{dQ}{dt} = \varepsilon_o  \cfrac{d\phi_E}{dt}$According to Maxwell's Ampere circuital Law, the line integral of magnetic field along a closed path is equal to $\mu_o$ times the total current.$\oint \vec B . \vec {dl} = \mu_o (i_c + i_d)$where $i_c:$ Conduction current           $i_d:$ Displacement current$\oint \vec B . \vec {dl} = \mu_o (i_c + \varepsilon_o\cfrac{d\phi}{dt})$

Question 3

The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is:

Accepted Answer

The intensity of an electromagnetic wave is given by:$I=U_{av}c$here, $U_{av}$ is the average energy and $c$ is the speed of light.The average energy in terms of the electric field is written as:$U_{av}=\dfrac 12\varepsilon_oE_o^2$Average energy in terms of magnetic field:$U_{av}=\dfrac 12\dfrac{B_o^2}{\mu_o}$We know that, $E_o=cB_o$ and $c=\dfrac{1}{\sqrt{\mu_o\varepsilon_o}}$$\therefore U_{av\ (electric\ field)}=\dfrac 12\varepsilon_o\times\dfrac{1}{\mu_o\varepsilon_o}B_o^2$$\Rightarrow\dfrac 12\dfrac{B_o^2}{\mu_o}$Since the energy due to electric and magnetic field is same. so, both will have the same contribution to the intensity.

Question 4

The rms value of the electric field of the light coming from sun is 720 N $C^{-1}$. The average total energy density of the electromagnetic wave is

Accepted Answer

Given: The RMS value of the electric field of light is $720\ N/C$.Energy density of electromagnetic wave is given by:$E=\epsilon_0 E_{rms}^2$     $=8.85\times 10^{-12}\times (720)^2$$E\approx 4.58\times 10^{-6}J/m^3$Option $(B)$ is corret.

Question 5

Magnetic field in a plane electromagnetic wave is given by $ \overrightarrow{B} = B_0 sin (kx + \omega t) \hat{j} T $Expression for corresponding electric field will be :Where c is speed of light.

Accepted Answer

$\dfrac{\overrightarrow{E}}{\overrightarrow{B}}=C$$\overrightarrow{B} = B_0\sin(kx + \omega t)$$\overrightarrow {E} = B_0C\sin(kx+\omega t)\hat k$ $V/m$

Question 6

The amplitude of the magnetic field of a harmonic electromagnetic wave in vacuum is ${B}_{0}$ = 510 nT. The amplitude of the electric field part of the wave is

Accepted Answer

Given,$B_0=510nT$$c=3\times 10^8m/s$The magnitude of electric field is given by$E_0=B_0 c$$E_0=510\times 10^{-9}\times 3\times 10^8$$E_0=153NC^{-1}$The correct option is D.

Question 7

Define displacement current.

Accepted Answer

In electromagnetism, displacement current is a quantity appearing in Maxwell's equations that is defined in terms of the rate of change of electric displacement field. Displacement current has the units of electric current density, and it has an associated magnetic field just as actual currents do.It is mathematically represented as $I_{d} = \epsilon_{0} \dfrac {d\phi_{E}}{dt}$.

Question 8

A parallel plate capacitor with circular plates of radius $R$ is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between $\cfrac{R}{2}$ and $R$ is given by

Accepted Answer

Displacement current is given by &#10;&#10;  $ I={{\varepsilon&#10;}_{0}}\dfrac{d{{\phi }_{e}}}{dt} $ &#10;&#10; $ =\,{{\varepsilon&#10;}_{0}}A\dfrac{dE}{dt}\,\,\,\,(\because \,\phi =A.E) $ &#10;&#10; $&#10;=A\dfrac{d}{dt}\left(\dfrac{q}{{{A}^{'}}}\right) $ &#10;&#10; $&#10;=\dfrac{A}{{{A}^{'}}}i\,\,(\because \dfrac{dq}{dt}=i) $ &#10;&#10; $ =\dfrac{\pi&#10;{{\left(\dfrac{R}{2}\right)}^{2}}}{\pi {{R}^{2}}} $ &#10;&#10; $ =\dfrac{1}{4}i $ &#10;&#10;

Question 9

Maxwell's modified form of Ampere's circuital law is

Accepted Answer

$Answer:-$ DTreating all charges on the same footing (disregarding whether they are bound or free charges), the generalized Amp&#232;re's equation, also called the Maxwell&#8211;Amp&#232;re equation, is in integral form.

Question 10

Do electromagnetic waves carry energy and momentum?

Accepted Answer

Yes, EM waves carry energy E and momentum P. As electromagnetic waves contain both electric and magnetic fields, there is a non-zero energy density associated with it.

Revise with Concepts

Displacement Current

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Displacement Current

Maxwell's Electromagnetic Theory

List the properties of electromagnetic waves.

What is displacement current? Obtain an expression of displacement current for a charged capacitor. Write Ampere-Maxwell's law.

The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is:

The rms value of the electric field of the light coming from sun is 720 N $C^{- 1}$ . The average total energy density of the electromagnetic wave is

Magnetic field in a plane electromagnetic wave is given by
$B = B_{0} s i n (k x + ω t) \hat{j} T$
Expression for corresponding electric field will be :
Where c is speed of light.

The amplitude of the magnetic field of a harmonic electromagnetic wave in vacuum is $B_{0}$ = 510 nT. The amplitude of the electric field part of the wave is

Define displacement current.

A parallel plate capacitor with circular plates of radius $R$ is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between $\frac{R}{2}$ and $R$ is given by

Maxwell's modified form of Ampere's circuital law is

Do electromagnetic waves carry energy and momentum?

Revise with Concepts

Displacement Current

Quick Summary With Stories

Displacement Current

Maxwell's Electromagnetic Theory

List the properties of electromagnetic waves.

What is displacement current? Obtain an expression of displacement current for a charged capacitor. Write Ampere-Maxwell's law.

The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is:

The rms value of the electric field of the light coming from sun is 720 N C−1. The average total energy density of the electromagnetic wave is

Magnetic field in a plane electromagnetic wave is given by B=B0​sin(kx+ωt)j^​T Expression for corresponding electric field will be : Where c is speed of light.

The amplitude of the magnetic field of a harmonic electromagnetic wave in vacuum is B0​ = 510 nT. The amplitude of the electric field part of the wave is

Define displacement current.

A parallel plate capacitor with circular plates of radius R is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between 2R​ and R is given by

Maxwell's modified form of Ampere's circuital law is

Do electromagnetic waves carry energy and momentum?

The rms value of the electric field of the light coming from sun is 720 N $C^{- 1}$ . The average total energy density of the electromagnetic wave is

Magnetic field in a plane electromagnetic wave is given by
$B = B_{0} s i n (k x + ω t) \hat{j} T$
Expression for corresponding electric field will be :
Where c is speed of light.

The amplitude of the magnetic field of a harmonic electromagnetic wave in vacuum is $B_{0}$ = 510 nT. The amplitude of the electric field part of the wave is

A parallel plate capacitor with circular plates of radius $R$ is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between $\frac{R}{2}$ and $R$ is given by