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Q. No.In a plane electromagnetic wave travelling in free space, the electric field component oscillates sinusoidally at a frequency of \(2.0\times 10^{10}~ \mathrm{Hz}\) and amplitude \(48~\mathrm{Vm^{-1}}\). Then the amplitude of oscillating magnetic field is: (Speed of light in free space \(3\times 10^{8}~ \mathrm{ms^{-1}}\) )
1. \(1.6 \times 10^{-6} \mathrm{~T}\)
2. \(1.6 \times 10^{-9} \mathrm{~T}\)
3. \(1.6 \times 10^{-8} \mathrm{~T}\)
4. \(1.6 \times 10^{-7} \mathrm{~T}\)
1. \(1.6 \times 10^{-6} \mathrm{~T}\)
2. \(1.6 \times 10^{-9} \mathrm{~T}\)
3. \(1.6 \times 10^{-8} \mathrm{~T}\)
4. \(1.6 \times 10^{-7} \mathrm{~T}\)
Subtopic: Properties of EM Waves |
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\(\varepsilon_0\) and \(\mu_0\) are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are \(2\varepsilon_0\) and \(1.5\mu_0\) respectively, the refractive index of the medium will nearly be:
1. \(\sqrt2\)
2. \(\sqrt3\)
3. \(3\)
4. \(2\)
1. \(\sqrt2\)
2. \(\sqrt3\)
3. \(3\)
4. \(2\)
Subtopic: Properties of EM Waves |
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To produce an instantaneous displacement current of \(2~\mathrm{mA}\) in the space between the parallel plates of a capacitor of capacitance \(4~\mu F,\) the rate of change of applied variable potential difference \(\Big(\frac{dV}{dt}\Big)\) must be:
1. \( 800 \mathrm{~V} / \mathrm{s} \)
2. \( 500 \mathrm{~V} / \mathrm{s} \)
3. \( 200 \mathrm{~V} / \mathrm{s} \)
4. \( 400 \mathrm{~V} / \mathrm{s}\)
1. \( 800 \mathrm{~V} / \mathrm{s} \)
2. \( 500 \mathrm{~V} / \mathrm{s} \)
3. \( 200 \mathrm{~V} / \mathrm{s} \)
4. \( 400 \mathrm{~V} / \mathrm{s}\)
Subtopic: Displacement Current |
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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) \(10^{-10}~\mathrm{m}\) |
| (b) Microwaves | (ii) \(10^{2} \mathrm{~m}\) |
| (c) Infrared radiation | (iii) \(10^{-2} \mathrm{~m}\) |
| (d) X-rays | (iv) \(10^{-4} \mathrm{~m}\) |
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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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:
(\(\text{c}\) = velocity of light in vacuum)
1. \(v=\frac{\mathrm{c}}{\sqrt{\epsilon_{r} \mu_{\mathrm{r}}}}\)
2. \(v=\mathrm{c}\)
3. \(v=\sqrt{\frac{\mu_{\mathrm{r}}}{\epsilon_{\mathrm{r}}}}\)
4. \(v=\sqrt{\frac{\epsilon_{\mathrm{r}}}{\mu_{\mathrm{r}}}}\)
(\(\text{c}\) = velocity of light in vacuum)
1. \(v=\frac{\mathrm{c}}{\sqrt{\epsilon_{r} \mu_{\mathrm{r}}}}\)
2. \(v=\mathrm{c}\)
3. \(v=\sqrt{\frac{\mu_{\mathrm{r}}}{\epsilon_{\mathrm{r}}}}\)
4. \(v=\sqrt{\frac{\epsilon_{\mathrm{r}}}{\mu_{\mathrm{r}}}}\)
Subtopic: Properties of EM Waves |
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If \(\lambda_X,\lambda_I,\lambda_M\) and \(\lambda_\gamma\) are the wavelengths of \(X\)-rays, infrared rays, microwaves and \(\gamma\)-rays respectively, then:
| 1. | \(\lambda_\gamma<\lambda_X<\lambda_I<\lambda_M\) |
| 2. | \(\lambda_M<\lambda_I<\lambda_X<\lambda_\gamma\) |
| 3. | \(\lambda_X<\lambda_\gamma<\lambda_M<\lambda_I\) |
| 4. | \(\lambda_X<\lambda_I<\lambda_\gamma<\lambda_M\) |
Subtopic: Electromagnetic Spectrum |
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An electromagnetic wave is moving along negative \(\text{z (-z)}\) direction and at any instant of time, at a point, its electric field vector is \(3\hat j~\text{V/m}\). The corresponding magnetic field at that point and instant will be: (Take \(c=3\times10^{8}~\text{ms}^{-1}\) )
1. \(10\hat i~\text{nT}\)
2. \(-10\hat i~\text{nT}\)
3. \(\hat i~\text{nT}\)
4. \(-\hat i~\text{nT}\)
Subtopic: Properties of EM Waves |
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The magnetic field of a plane electromagnetic wave
is given by,
\(\vec B=3\times10^{-8}cos(1.6\times10^3x+48\times10^{10}t)\hat j~T.\)
The associated electric field will be:
is given by,
\(\vec B=3\times10^{-8}cos(1.6\times10^3x+48\times10^{10}t)\hat j~T.\)
The associated electric field will be:
| 1. | \(3 \times 10^{-8} \cos \left(1.6 \times 10^3 x+48 \times 10^{10} t\right) \hat{i}~\text{ V/m}\) |
| 2. | \(3 \times 10^{-8} \sin \left(1.6 \times 10^3 \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{i}}~ \mathrm{V} / \mathrm{m}\) |
| 3. | \(9 \sin \left(1.6 \times 10^3 \mathrm{x}-48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{k}} ~~\mathrm{V} / \mathrm{m}\) |
| 4. | \(9 \cos \left(1.6 \times 10^3 \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{k}}~~\mathrm{V} / \mathrm{m}\) |
Subtopic: Properties of EM Waves |
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The ratio of the magnitude of the magnetic field and electric field intensity of a plane electromagnetic wave in free space of permeability \(\mu_0\) and permittivity \(\varepsilon_0\) is:
(Given that \(c=\) velocity of light in free space)
1. \(c\)
2. \(\frac1c\)
3. \(\frac{c}{\sqrt{\mu_0\varepsilon_0}}\)
4. \(\frac{\sqrt{\mu_0\varepsilon_0}}{c}\)
(Given that \(c=\) velocity of light in free space)
1. \(c\)
2. \(\frac1c\)
3. \(\frac{c}{\sqrt{\mu_0\varepsilon_0}}\)
4. \(\frac{\sqrt{\mu_0\varepsilon_0}}{c}\)
Subtopic: Properties of EM Waves |
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For a plane electromagnetic wave propagating in the x-direction, which one of the following combinations gives the correct possible directions for the electric field \((E)\) and magnetic field \((B)\) respectively?
1. \(\hat{j}+\hat{k},~-\hat{j}-\hat{k}\)
2. \(-\hat{j}+\hat{k},~-\hat{j}+\hat{k}\)
3. \(\hat{j}+\hat{k},~\hat{j}+\hat{k}\)
4. \(-\hat{j}+\hat{k},~-\hat{j}-\hat{k}\)
Subtopic: Properties of EM Waves |
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