Q. No.A magnetic field vector in an electromagnetic wave is represented by \(\vec{B}=B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{j} .\) Its associated electric field vector is:
1. \(\vec{E}=-v \lambda B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{k}\)
2. \(\vec{E}=-v \lambda B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{i}\)
3. \(\vec{E}=v \lambda B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{k}\)
4. \(\vec{E}=v \lambda B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{i}\)
1. \(\vec{E}=-v \lambda B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{k}\)
2. \(\vec{E}=-v \lambda B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{i}\)
3. \(\vec{E}=v \lambda B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{k}\)
4. \(\vec{E}=v \lambda B_0 \sin \left(2 \pi v t-\dfrac{2 \pi x}{\lambda}\right) \hat{i}\)
Subtopic: Properties of EM Waves |
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Level 2: 60%+
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An electromagnetic wave travels in free space along the \(x\text-\)direction. At a particular point in space and time, \(\vec{B}=2 \times 10^{-7} \hat{j} ~\text{T}\) is associated with this wave. The value of corresponding electric field \(\vec{E}\) at this point is: (in \(\text{V/m}.\))
1. \(60 \hat{k}~ \)
2. \(-60 \hat{k} \)
3. \( 30 \hat{k}\)
4. \(-600 \hat{k}\)
1. \(60 \hat{k}~ \)
2. \(-60 \hat{k} \)
3. \( 30 \hat{k}\)
4. \(-600 \hat{k}\)
Subtopic: Properties of EM Waves |
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For an electromagnetic wave propagating through vacuum, \(\vec{k},\vec{E}\) and \(\omega\) represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by:
1. \(\dfrac{\vec{E} \times \vec{k}}{\omega}\)
2. \(\dfrac{\vec{k} \times \vec{E}}{\omega}\)
3. \(\omega(\vec{E} \times \vec{k})\)
4. \(\omega(\vec{k} \times \vec{E})\)
1. \(\dfrac{\vec{E} \times \vec{k}}{\omega}\)
2. \(\dfrac{\vec{k} \times \vec{E}}{\omega}\)
3. \(\omega(\vec{E} \times \vec{k})\)
4. \(\omega(\vec{k} \times \vec{E})\)
Subtopic: Properties of EM Waves |
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Level 3: 35%-60%
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A point light source emits E.M. waves in free space. A detector, placed at a distance of \(L~\text{m},\) \(45^\circ\)
1. \(\dfrac{I_0}{4}\)
2. \( I_0\)
3. \(\dfrac{I_0}{\sqrt{2}} \)
4. \(\dfrac{I_0}{2}\)
1. \(\dfrac{I_0}{4}\)
2. \( I_0\)
3. \(\dfrac{I_0}{\sqrt{2}} \)
4. \(\dfrac{I_0}{2}\)
Subtopic: Properties of EM Waves |
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An electromagnetic wave travelling in \(x\text-\)direction is described by field equation \({E}_y=300 \sin \omega\left(t-\dfrac{x}{{c}}\right)\). If the electron is restricted to move in \(y\text-\)direction only with speed of \(1.5\times 10^6~\text{m/s}\) then ratio of maximum electric and magnetic forces on the electron is:
1. \(200\)
2. \(150\)
3. \(400\)
4. \(300\)
1. \(200\)
2. \(150\)
3. \(400\)
4. \(300\)
Subtopic: Properties of EM Waves |
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Level 3: 35%-60%
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Given below are two statements:
In the light of the above statements, choose the correct answer from the options given below:
| Assertion (A): | The electromagnetic wave exerts pressure on the surface on which they are allowed to fall. |
| Reason (R): | There is no mass associated with the electromagnetic waves. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Properties of EM Waves |
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The electric field a plane electromagnetic wave is given by :
\({E}_{y}=69 \sin \left[0.6 \times 10^3 {x}-1.8 \times 10^{11} {t}\right] ~\text{V/m}.\)
The expression for magnetic field associated with this electromagnetic wave is: (in T)
\({E}_{y}=69 \sin \left[0.6 \times 10^3 {x}-1.8 \times 10^{11} {t}\right] ~\text{V/m}.\)
The expression for magnetic field associated with this electromagnetic wave is: (in T)
| 1. | \(B_z=2.3 \times 10^{-7} \sin \left[0.6 \times 10^3 x-1.8 \times 10^{11} t\right]\) |
| 2. | \(B_z=2.3 \times 10^{-7} \sin \left[0.6 \times 10^3 x+1.8 \times 10^{11} t\right]\) |
| 3. | \(B_y=69 \sin \left[0.6 \times 10^3 x+1.8 \times 10^{11} t\right]\) |
| 4. | \( B_y=2.3 \times 10^{-7} \sin \left[0.6 \times 10^3 x-1.8 \times 10^{11} t\right] \) |
Subtopic: Properties of EM Waves |
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The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, \(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right)~\text{V/m}\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is:
(Speed of light in free space is \(3\times10^8 ~\text{m/s})\)
1. \(6\)
2. \(4\)
3. \(5\)
4. \(7\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is:
(Speed of light in free space is \(3\times10^8 ~\text{m/s})\)
1. \(6\)
2. \(4\)
3. \(5\)
4. \(7\)
Subtopic: Properties of EM Waves |
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A laser beam has intensity of \(4.0\times10^{14}~ \text{W/m}^2.\) The amplitude of magnetic field associated with beam is: (in \(\text{T}\))
(Take \(\varepsilon_0= 8.85\times 10^{-12} ~\text{C}^2/\text{Nm}^2\) and \(c = 3\times10^8 ~\text{m/s})\)
1. \(2.0\)
2. \(18.3\)
3. \(5.5\)
4. \(1.83\)
(Take \(\varepsilon_0= 8.85\times 10^{-12} ~\text{C}^2/\text{Nm}^2\) and \(c = 3\times10^8 ~\text{m/s})\)
1. \(2.0\)
2. \(18.3\)
3. \(5.5\)
4. \(1.83\)
Subtopic: Properties of EM Waves |
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The equation of the electric field of an electromagnetic wave propagating through free space is given by:
\({E}=\sqrt{377} \sin \left(6.27 \times 10^3 {t}-2.09 \times 10^{-5} {x}\right)~ \text{N/C}\)
The average power of the electromagnetic wave is:
\(\left(\dfrac{1}{\alpha}\right) \text{W/m}^2\). The value of \(\alpha\) is:
\(\left(\text { Take } \sqrt{\dfrac{\mu_0}{\varepsilon_0}}=377 \text { in SI units }\right)\)
1. \(3\)
2. \(4\)
3. \(2\)
4. \(5\)
\({E}=\sqrt{377} \sin \left(6.27 \times 10^3 {t}-2.09 \times 10^{-5} {x}\right)~ \text{N/C}\)
The average power of the electromagnetic wave is:
\(\left(\dfrac{1}{\alpha}\right) \text{W/m}^2\). The value of \(\alpha\) is:
\(\left(\text { Take } \sqrt{\dfrac{\mu_0}{\varepsilon_0}}=377 \text { in SI units }\right)\)
1. \(3\)
2. \(4\)
3. \(2\)
4. \(5\)
Subtopic: Properties of EM Waves |
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