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Q. No.The maximum electric field of a plane electromagnetic wave traveling through a vacuum is \(300~\text{V/m}.\) The maximum magnetic field of this wave is:
1. \(300~\text{T}\)
2. \(10^{-6}~\text{T}\)
3. \(9 \times 10^{10}~\text{T}\)
4. \(300\sqrt {2}~\text{T}\)
Subtopic: Â Properties of EM Waves |
 87%
Level 1: 80%+
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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. \(\hat{j} + \hat{k}\)
1. \(\hat {i}\)
2. \(\hat {j}\)
3. \(\hat{k} \)
4. \(\hat{j} + \hat{k}\)
Subtopic: Â Properties of EM Waves |
 74%
Level 2: 60%+
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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 |
Level 3: 35%-60%
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The electric field of an electromagnetic wave is given by \(\overrightarrow E = E_0 \hat j \cos (\omega t - kx)+ E_0\hat i \sin (\omega t -kx) \).
The maximum value of the electric field in the wave is:
The maximum value of the electric field in the wave is:
| 1. | \(\dfrac {E_0} {\sqrt 2}\) | 2. | \(E_0\) |
| 3. | \(\sqrt 2 E_0\) | 4. | \(\sqrt 3 E_0\) |
Subtopic: Â Properties of EM Waves |
Level 3: 35%-60%
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The average electric field associated with the plane electromagnetic wave \(\vec E = E_0 \hat {i} \sin (wt - kz)\) is:
| 1. | \(E_0 \hat i\) | 2. | \(\dfrac {E_0} { \sqrt 2}\) \(\hat i \) |
| 3. | \(\sqrt 2E_0 \hat i\) | 4. | zero |
Subtopic: Â Properties of EM Waves |
 54%
Level 3: 35%-60%
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Which of the following situation(s), can cause the radiation of an electromagnetic wave?
Choose the correct option from the given ones:
| (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 option from the given ones:
| 1. | only (A) |
| 2. | only (B) |
| 3. | only (A) & (B) |
| 4. | (A), (B), (C) |
Subtopic: Â Generation of EM Waves |
 66%
Level 2: 60%+
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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%
Level 2: 60%+
Hints
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%
Level 2: 60%+
Hints
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 |
 76%
Level 2: 60%+
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Match List I with List II.
Choose the correct answer from the options given below:
| List - I (Electromagnetic waves) |
List - II (Wavelength) |
||
| (a) | AM radio waves | (i) | \(10^{-10}~\text{m}\) |
| (b) | Microwaves | (ii) | \(10^{2} ~\text{m}\) |
| (c) | Infrared radiation | (iii) | \(10^{-2} ~\text{m}\) |
| (d) | \(X\)-rays | (iv) | \(10^{-4} ~\text{m}\) |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (ii) | (iii) | (iv) | (i) |
| 2. | (iv) | (iii) | (ii) | (i) |
| 3. | (iii) | (ii) | (i) | (iv) |
| 4. | (iii) | (iv) | (ii) | (i) |
Subtopic: Â Electromagnetic Spectrum |
 74%
Level 2: 60%+
NEET - 2022
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