Electromagnetic Waves, Energy and Momentum - Electromagnetic theory - Physics Previous Year Questions

1

2007 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2007

An electromagnetic wave with \( \vec{E}(\vec{x}, t) = E_0 \cos(\omega t - k z) \hat{i} \) is traveling in free space and crosses a disc of radius 2 m placed perpendicular to the z-axis. If \( E_0 = 60 \text{ V m}^{-1} \), the average power, in Watt, crossing the disc along the z-direction is

A

30

B

60

C

120

D

270

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2

2008 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2008

A parallel plate capacitor is being discharged. What is the direction of the energy flow in terms of the Poynting vector in the space between the plates?

A

Along the wire in the positive z axis

B

Radially inward (\(-\hat{r}\))

C

Radially outward (\(\hat{r}\))

D

Circumferential (\(\hat{\phi}\))

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3

2008 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2008

A plane electromagnetic wave is given by \( E_0 (\hat{x} + e^{i\delta} \hat{y}) \exp[i(kz - \omega t)] \). At a given location, the number of times \( \vec{E} \) vanishes in one second is

A

An integer near \(\frac{\omega}{\pi} \) when \(\delta = n\pi \) and zero when \(\delta \neq n\pi \), \(n \) is integer

B

An integer near \(\frac{\omega}{\pi} \) and is independent of \(\delta \)

C

An integer near \(\frac{\omega}{2\pi} \) when \(\delta = n\pi \) and zero when \(\delta \neq n\pi \), \(n \) is integer

D

An integer near \(\frac{\omega}{2\pi} \) and is independent of \(\delta \)

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4

2008 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2008

A nonrelativistic charged particle moves along the positive \(x\)-axis with a constant positive acceleration \(a\hat{x}\). The particle is at the origin at \(t = 0\). Radiation is observed at \(t = 0\) at a distant point \((0, d, 0)\) on the \(y\)-axis. Which one of the following statements is correct?

A

The radiation is unpolarized.

B

The radiation is plane polarized with polarization parallel to the \(x\)-axis.

C

The radiation is plane polarized with polarization parallel to the \(xy\) plane along a line inclined to the \(x\) axis.

D

The radiation is elliptically polarized.

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5

2010 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2010

Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is

A

Always independent of frequency

B

Monotonically decreasing with frequency

C

Monotonically increasing with frequency

D

A non-monotonic function of frequency

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6

2010 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2010

If \(\varepsilon\) and \(\mu\) assume negative values in a certain frequency range, then the directions of the propagation vector \(\vec{k}\) and the Poynting vector \(\vec{S}\) in that frequency range are related as

A

\(\vec{k}\) and \(\vec{S}\) are parallel

B

\(\vec{k}\) and \(\vec{S}\) are anti-parallel

C

\(\vec{k}\) and \(\vec{S}\) are perpendicular to each other

D

\(\vec{k}\) and \(\vec{S}\) make an angle that depends on the magnitude of \(|\varepsilon|\) and \(|\mu|\)

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7

2011 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2011

The electric field \(\vec{E}(x,y,z,t)\) corresponding to the above wave is given by

A

\(c B_0 \sin \left[ (x+y) \frac{k}{\sqrt{2}} + \omega t \right] \frac{(\hat{i} - \hat{j})}{\sqrt{2}}\)

B

\(c B_0 \sin \left[ (x+y) \frac{k}{\sqrt{2}} + \omega t \right] \frac{(\hat{i} + \hat{j})}{\sqrt{2}}\)

C

\(c B_0 \sin \left[ (x+y) \frac{k}{\sqrt{2}} + \omega t \right] \hat{i}\)

D

\(c B_0 \sin \left[ (x+y) \frac{k}{\sqrt{2}} + \omega t \right] \hat{j}\)

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8

2011 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2011

The average Poynting vector is given by

A

\(\frac{c B_0^2}{2\mu_0} \frac{(\hat{i} - \hat{j})}{\sqrt{2}}\)

B

\(-\frac{c B_0^2}{2\mu_0} \frac{(\hat{i} - \hat{j})}{\sqrt{2}}\)

C

\(\frac{c B_0^2}{2\mu_0} \frac{(\hat{i} + \hat{j})}{\sqrt{2}}\)

D

\(-\frac{c B_0^2}{2\mu_0} \frac{(\hat{i} + \hat{j})}{\sqrt{2}}\)

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9

2012 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2012

The space-time dependence of the electric field of a linearly polarized light in free space is given by $xE_0 \cos(\omega t - kz)$ where $E_0$, $\omega$ and $k$ are the amplitude, the angular frequency and the wavevector, respectively. The time averaged energy density associated with the electric field is

A

$\frac{1}{4}\epsilon_0 E_0^2$

B

$\frac{1}{2}\epsilon_0 E_0^2$

C

$\epsilon_0 E_0^2$

D

$2\epsilon_0 E_0^2$

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10

2012 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2012

A plane electromagnetic wave traveling in free space is incident normally on a glass plate of refractive index 3/2. If there is no absorption by the glass, its reflectivity is

A

4%

B

16%

C

20%

D

50%

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11

2012 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2012

A plane polarized electromagnetic wave in free space at time t = 0 is given by E⃗(x,z) = 10ĵ exp[i(6x + 8z)]. The magnetic field B⃗(x,z,t) is given by

A

B⃗(x,z,t) = (1/c)(6k̂ - 8î) exp[i(6x + 8z - 10ct)]

B

B⃗(x,z,t) = (1/c)(6k̂ + 8î) exp[i(6x + 8z - 10ct)]

C

B⃗(x,z,t) = (1/c)(6k̂ - 8î) exp[i(6x + 8z - ct)]

D

B⃗(x,z,t) = (1/c)(6k̂ + 8î) exp[i(6x + 8z + ct)]

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12

2013 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2013

A circularly polarized monochromatic plane wave is incident on a dielectric interface at Brewster angle. Which one of the following statements is CORRECT?

A

The reflected light is plane polarized in the plane of incidence and the transmitted light is circularly polarized.

B

The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is plane polarized in the plane of incidence.

C

The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is elliptically polarized.

D

There will be no reflected light and the transmitted light is circularly polarized.

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13

2013 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2013

A monochromatic plane wave at oblique incidence undergoes reflection at a dielectric interface. If \( \hat{k}_i \), \( \hat{k}_r \) and \( \hat{n} \) are the unit vectors in the directions of incident wave, reflected wave and the normal to the surface respectively, which one of the following expressions is correct?

A

\((\hat{k}_i - \hat{k}_r) \times \hat{n} \neq 0 \)

B

\((\hat{k}_i - \hat{k}_r) \cdot \hat{n} = 0 \)

C

\((\hat{k}_i \times \hat{n}) \cdot \hat{k}_r = 0 \)

D

\((\hat{k}_i \times \hat{n}) \cdot \hat{k}_r \neq 0 \)

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14

2014 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2014

The electric field of a uniform plane wave propagating in a dielectric, non-conducting medium is given by, \(\vec{E} = \hat{x} 10 \cos(6\pi \times 10^7 t - 0.4\pi z)\) V/m. The phase velocity of the wave is _____________ \(\times 10^8\) m/s.

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15

2014 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2014

The intensity of a laser in free space is 150 mW/m². The corresponding amplitude of the electric field of the laser is _________ V/m. (ε₀ = 8.854 × 10⁻¹² C²/N.m²)

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16

2016 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2016

The electric field component of a plane electromagnetic wave travelling in vacuum is given by \(\vec{E}(z,t) = E_0 \cos(kz - \omega t)\hat{i}\). The Poynting vector for the wave is

A

\((c\epsilon_0/2)E_0^2 \cos^2(kz - \omega t)\hat{j}\)

B

\((c\epsilon_0/2)E_0^2 \cos^2(kz - \omega t)\hat{k}\)

C

\(c\epsilon_0 E_0^2 \cos^2(kz - \omega t)\hat{j}\)

D

\(c\epsilon_0 E_0^2 \cos^2(kz - \omega t)\hat{k}\)

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17

2017 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2017

A monochromatic plane wave in free space with electric field amplitude of 1 V/m is normally incident on a fully reflecting mirror. The pressure exerted on the mirror is ______ \( \times 10^{-12} \) Pa. (up to two decimal places) (\( \varepsilon_0 = 8.854 \times 10^{-12} \) F/m).

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18

2018 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2018

A light beam of intensity \( I_0 \) is falling normally on a surface. The surface absorbs 20% of the intensity and the rest is reflected. The radiation pressure on the surface is given by \( X I_0 / c \), where \( X \) is ___________ (up to one decimal place). Here \( c \) is the speed of light.

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19

2018 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2018

A long straight wire, having radius \(a\) and resistance per unit length \(r\), carries a current \(I\). The magnitude and direction of the Poynting vector on the surface of the wire is

A

\(I^2 r / 2\pi a\) , perpendicular to axis of the wire and pointing inwards

B

\(I^2 r / 2\pi a\) , perpendicular to axis of the wire and pointing outwards

C

\(I^2 r / \pi a\) , perpendicular to axis of the wire and pointing inwards

D

\(I^2 r / \pi a\) , perpendicular to axis of the wire and pointing outwards

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20

2018 · Physics · Electromagnetic theory · Electromagnetic Waves, Energy and Momentum

Physics (PH) 2018

An electromagnetic plane wave is propagating with an intensity \(I = 1.0 \times 10^5 \text{ Wm}^{-2}\) in a medium with \(\epsilon = 3\epsilon_0\) and \(\mu = \mu_0\). The amplitude of the electric field inside the medium is ______ \(\times 10^3 \text{ Vm}^{-1}\) (up to one decimal place). \((\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}, \mu_0 = 4\pi \times 10^{-7} \text{ NA}^{-2}, c = 3 \times 10^8 \text{ ms}^{-1})\)

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