Q. No.Assume a bulb of efficiency \(2.5\%\) as a point source. The peak values of the electric field and magnetic field produced by the radiation coming from a \(100~\text{W}\) bulb at a distance of \(3~\text{m}\) are respectively:
| 1. | \( 2.5 ~\text{V/m}, ~2.2 \times 10^{-8} ~\text{T} \) |
| 2. | \( 3.6 ~\text{V/m}, ~ 3.6 ~\text{T} \) |
| 3. | \( 4.07~\text{V/m},~ 1.4 \times 10^{-8} ~\text{T}\) |
| 4. | \( 4.2 ~\text{V/m}, ~3.4 \times 10^{-6}~\text{T}\) |
Subtopic: Â Properties of EM Waves |
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The magnetic field in a plane electromagnetic wave is given by \(\mathrm{B}=\left(2 \times 10^{-7}\right) \mathrm{T} \sin \left(0.5 \times 10^3 \mathrm{x}+1.5 \times 10^{11} \mathrm{t}\right )\). The wavelength and frequency of the wave are respectively:
| 1. | \( 2.16 \mathrm{~cm}, 24.1 \mathrm{~GHz} \) |
| 2. | \( 0.29 \mathrm{~cm}, 13.7 \mathrm{~GHz} \) |
| 3. | \( 3.23 \mathrm{~cm}, 20.0 \mathrm{~GHz} \) |
| 4. | \( 1.26 \mathrm{~cm}, 23.9 \mathrm{~GHz}\) |
Subtopic: Â Properties of EM Waves |
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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:
1. \(E_0 \over \sqrt 2\)
2. \(E_o\)
3. \(\sqrt 2 E_0\)
4. \(\sqrt 3 E_0\)
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: Â Properties of EM Waves |
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When light propagates through a material medium of relative permittivity, \(\epsilon_{r}\) and relative permeability, \(\mu_{r}\) the velocity of light, \(v\) is given by:
(\(c\) = velocity of light in vacuum)
1. \(v=\frac{{c}}{\sqrt{\epsilon_{r} \mu_{{r}}}}\)
2. \(v={c}\)
3. \(v=\sqrt{\frac{\mu_{{r}}}{\epsilon_{{r}}}}\)
4. \(v=\sqrt{\frac{\epsilon_{{r}}}{\mu_{{r}}}}\)
(\(c\) = velocity of light in vacuum)
1. \(v=\frac{{c}}{\sqrt{\epsilon_{r} \mu_{{r}}}}\)
2. \(v={c}\)
3. \(v=\sqrt{\frac{\mu_{{r}}}{\epsilon_{{r}}}}\)
4. \(v=\sqrt{\frac{\epsilon_{{r}}}{\mu_{{r}}}}\)
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. \(f_t\neq f_0\)
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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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: Â 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: Â 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: Â 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: Â 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)
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