Q. No.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:
1.
\(\dfrac {E_0} { \sqrt 2}\)
2.
\(\sqrt 2~ E_0\)
3.
\(E_o\)
4.
\(2E_o\)
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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 |
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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. |
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| 1. | \(\dfrac{L}{T}\) | 2. | \(\dfrac{2L}{T}\) |
| 3. | \(\dfrac{L}{2T}\) | 4. | \(\dfrac{\sqrt3L}{T}\) |
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| (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) |
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1. \(\dfrac{P}{c}\)
2. \(\dfrac{P}{2c}\)
3. \(\dfrac{\sqrt3P}{c}\)
4. \(\dfrac{\sqrt3P}{2c}\)
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| 1. | \(\hat {i}\) | 2. | \(\hat {j}\) |
| 3. | \(\hat{k} \) | 4. | \(\hat{j} + \hat{k}\) |
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| 1. | Zero |
| 2. | \(\lambda\) |
| 3. | \(n\lambda,\) where \(n\) is an integer |
| 4. | \(2n\lambda,\) where \(n\) is an integer |
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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 |
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\(\vec E_1(x,t)=E_1\hat j~\sin(\omega t-k_0x),\) 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. | \(2\sqrt2\) |
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