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Q. No.An electromagnetic waveform given by \(\vec{E}=E_{0} \hat{j} \sin \omega t\cos k x\) is set up in a certain region of space, where \(\vec{E}\) represents the electric field. The magnetic field associated with this waveform oscillates along the direction of:
1.
\(\hat {i}\)
2.
\(\hat {j}\)
3.
\(\hat{k} \)
4.
\(\hat{j} + \hat{k}\)
Subtopic: Â Properties of EM Waves |
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An electromagnetic waveform which has an electric field given by:
\(\vec{E}=E_{0}[\hat{\imath} \cos (\omega t-k z)+\hat{\jmath} \cos (\omega t-k x)]\) and the waveform propagates. The maximum electric field has the magnitude:
\(\vec{E}=E_{0}[\hat{\imath} \cos (\omega t-k z)+\hat{\jmath} \cos (\omega t-k x)]\) and the waveform propagates. The maximum electric field has the magnitude:
| 1. | \(\dfrac {E_0} { \sqrt 2}\) | 2. | \(\sqrt 2~ E_0\) |
| 3. | \(E_o\) | 4. | \(2E_o\) |
Subtopic: Â Properties of EM Waves |
 56%
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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:
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 |
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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 |
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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 |
 67%
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