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Q. No.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:
1. \(E_0 \over \sqrt 2\)
2. \(E_o\)
3. \(\sqrt 2 E_0\)
4. \(\sqrt 3 E_0\)
Subtopic: Properties of EM Waves |
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The maximum electric field of a plane electromagnetic wave travelling 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. \(300\sqrt {2}~\text{T}\)
1. \(300~\text{T}\)
2. \(10^{-6}~\text{T}\)
3. \(9 \times 10^{10}~\text{T}\)
4. \(300\sqrt {2}~\text{T}\)
Subtopic: Properties of EM Waves |
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An electromagnetic waveform given by: \(\vec{E}=E_{0} \hat{\jmath} \sin \omega t~ \cos k x\) is set up in a certain region of space, where \(\overrightarrow E\)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: Properties of EM Waves |
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A plane electromagnetic wave is given by its electric field: \(\overrightarrow E=\overrightarrow {E_0}~cos\frac{\omega}{c}(ct-\beta x)\)
where \(\omega\) and \(\beta\) are constants, \(t\) is the time and \(x\) represents the x-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-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: Properties of EM Waves |
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The average electric field associated with the plane electromagnetic wave \(\overrightarrow E = E_0 \hat {i} \sin (wt - kz)\) is:
1. \(E_0 \hat i\)
2. \(E_0 \over \sqrt 2\) \(\hat i \)
3. \(\sqrt 2E_0 \hat i\)
4. zero (null)
1. \(E_0 \hat i\)
2. \(E_0 \over \sqrt 2\) \(\hat i \)
3. \(\sqrt 2E_0 \hat i\)
4. zero (null)
Subtopic: Properties of EM Waves |
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Which of the following situation(s), can cause the radiation of an electromagnetic wave?
| (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 |
| 1. | only (A) |
| 2. | only (B) |
| 3. | only (A) & (B) |
| 4. | (A), (B), (C) |
Subtopic: Generation of EM Waves |
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A plane electromagnetic waveform given by: \(\overrightarrow E_1=E_0\hat j\sin(\omega t-kx)\)
propagates along the \(x\)-axis. A second waveform given by: \(\overrightarrow E_2=E_0\hat k\sin(\omega t-kx)\)
is also allowed to propagate. The magnetic field has the amplitude: (Assume speed of light in vacuum is \(c\))
1. \(\frac{E_0}{c}\)
2. \(\frac{E_0}{2c}\)
3. \(\frac{\sqrt2E_0}{c}\)
4. zero
propagates along the \(x\)-axis. A second waveform given by: \(\overrightarrow E_2=E_0\hat k\sin(\omega t-kx)\)
is also allowed to propagate. The magnetic field has the amplitude: (Assume speed of light in vacuum is \(c\))
1. \(\frac{E_0}{c}\)
2. \(\frac{E_0}{2c}\)
3. \(\frac{\sqrt2E_0}{c}\)
4. zero
Subtopic: 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:
1. \(2\)
2. \(\sqrt2\)
3. \(4\)
4. \(2\sqrt2\)
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: 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. \(f_t\neq f_0\)
1. \(f_t=f_0\)
2. \(f_t>f_0\)
3. \(f_t<f_0\)
4. \(f_t\neq f_0\)
Subtopic: Properties of EM Waves |
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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: Electromagnetic Spectrum |
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