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Q. No.Electromagnetic waveform given by the electric field: \(\vec E=E_0[\hat{i}+\hat{j}\cos(\omega t-kx)]\) is established in space.
The magnetic field associated with the wave has the amplitude:
1.
\(\dfrac{E_0}{c}\)
2.
\(\dfrac{2E_0}{c}\)
3.
\(\dfrac{\sqrt2E_0}{c}\)
4.
zero
Subtopic: Â Properties of EM Waves |
 59%
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A plane electromagnetic wave is given by its electric field: \(\vec {E}=\vec {E_0}\cos\dfrac{\omega}{c}(ct-\beta x)\)
where \(\omega\) and \(\beta\) are constants, \(t\) is the time and \(x\) represents the \(x\text-\)coordinate. \(c\) is the speed of the light in vacuum.
The value of \(\beta,\)
where \(\omega\) and \(\beta\) are constants, \(t\) is the time and \(x\) represents the \(x\text-\)coordinate. \(c\) is the speed of the light in vacuum.
The value of \(\beta,\)
| 1. | cannot be less than \(1\). |
| 2. | equals \(1\), always. |
| 3. | cannot be greater than \(1\). |
| 4. | can be any non-zero value. |
Subtopic: Â Properties of EM Waves |
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A plane electromagnetic wavefront is incident at an angle of \(30^{\circ}\) onto a flat surface. The difference between the arrival times of the wave at the points \(A\) and \(B\) is \(T,\) where \(AB=L.\) Then, the speed of the wavefront in the medium is:
| 1. | \(\dfrac{L}{T}\) | 2. | \(\dfrac{2L}{T}\) |
| 3. | \(\dfrac{L}{2T}\) | 4. | \(\dfrac{\sqrt3L}{T}\) |
Subtopic: Â Properties of EM Waves |
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Which of the following situation(s), can cause the radiation of an electromagnetic wave?
Choose the correct options:
| (A) | a varying sinusoidal current flowing through a capacitor |
| (B) | an electric dipole, whose size (and magnitude) is oscillating with time |
| (C) | a steady current flowing through a toroid |
Choose the correct options:
| 1. | only (A) |
| 2. | only (B) |
| 3. | only (A) & (B) |
| 4. | (A), (B), (C) |
Subtopic: Â Generation of EM Waves |
 66%
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An incident light beam of power \(P\) falls on a flat surface, at an angle of incidence of \(60^{\circ}.\) \(50\%\) of the beam is absorbed and the remaining reflected. The force exerted on the surface is:
| 1. | \(\dfrac{P}{c}\) | 2. | \(\dfrac{P}{2c}\) |
| 3. | \(\dfrac{\sqrt3P}{c}\) | 4. | \(\dfrac{\sqrt3P}{2c}\) |
Subtopic: Â Properties of EM Waves |
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In a plane polarised electromagnetic wave of wavelength \(\lambda,\) the electric field at a certain point \(P\) has the value \(\vec E_P(t).\) At a different point \(Q,\) the electric field is \(\vec E_Q(t).\) If \(\vec E_{P}\) and \(\vec E_{Q}\) are in phase with each other, then the component of \(\overrightarrow {PQ}\) along the direction of propagation equals:
| 1. | Zero |
| 2. | \(\lambda\) |
| 3. | \(n\lambda,\) where \(n\) is an integer |
| 4. | \(2n\lambda,\) where \(n\) is an integer |
Subtopic: Â Properties of EM Waves |
 53%
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A plane electromagnetic waveform given by: \(\vec {E}_1=E_0\hat j\sin(\omega t-kx)\)
propagates along the \(x\)-axis. A second waveform given by: \(\vec {E}_2=E_0\hat k\sin(\omega t-kx)\)
is also allowed to propagate. The magnetic field has the amplitude: (Assume speed of light in vacuum is \(c\))
propagates along the \(x\)-axis. A second waveform given by: \(\vec {E}_2=E_0\hat k\sin(\omega t-kx)\)
is also allowed to propagate. The magnetic field has the amplitude: (Assume speed of light in vacuum is \(c\))
| 1. | \(\dfrac{E_0}{c}\) | 2. | \(\dfrac{E_0}{2c}\) |
| 3. | \(\dfrac{\sqrt2E_0}{c}\) | 4. | Zero |
Subtopic: Â Properties of EM Waves |
 65%
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The region on the left of the \(y\)-axis \((x<0)\) represents vacuum, and the region on the right \((x>0)\) represents a transparent medium. An electromagnetic wave travelling along the \(x\)-axis given by:
\(\vec E_1(x,t)=E_1\hat j~\sin(\omega t-k_0x),\) where \(x<0,\)
is incident on to the medium on the right. The transmitted wave in the medium is:
\(\vec E_2(x,t)=E_2\hat j~\sin(\omega t-2k_0x),\) where \(x>0.\)
The refractive index of the medium is:
\(\vec E_1(x,t)=E_1\hat j~\sin(\omega t-k_0x),\) where \(x<0,\)
is incident on to the medium on the right. The transmitted wave in the medium is:
\(\vec E_2(x,t)=E_2\hat j~\sin(\omega t-2k_0x),\) where \(x>0.\)
The refractive index of the medium is:
| 1. | \(2\) | 2. | \(\sqrt2\) |
| 3. | \(4\) | 4. | \(2\sqrt2\) |
Subtopic: Â Properties of EM Waves |
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When an electromagnetic wave of frequency \(f_0\) undergoes refraction at the interface of two transparent (non-absorbing) media, the frequency of the transmitted wave is \(f_t.\) Then:
| 1. | \(f_t=f_0\) |
| 2. | \(f_t>f_0\) |
| 3. | \(f_t<f_0\) |
| 4. | \(f_t\neq f_0\) |
Subtopic: Â Properties of EM Waves |
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Given below are two statements:
| Statement I: | Electromagnetic waves are radiated when a charged particle undergoes SHM. |
| Statement II: | Electromagnetic waves propagate energy in the direction of the electric field of the wave. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Â Generation of EM Waves |
 61%
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