Q. No.Match List-I (Electromagnetic wave type) with List-II (Its association/application) and select the correct option from the choices given below the list:
| List-I | List-II | ||
| (a) | Infrared waves | (i) | To treat muscular strain |
| (b) | Radio waves | (ii) | For broadcasting |
| (c) | X-rays | (iii) | To detect fractures of bones |
| (d) | Ultraviolet rays | (iv) | Absorbed by the ozone layer of the atmosphere |
| Options: | (a) | (b) | (c) | (d) |
| 1. | (i) | (ii) | (iv) | (iii) |
| 2. | (iii) | (ii) | (i) | (iv) |
| 3. | (i) | (ii) | (iii) | (iv) |
| 4. | (iv) | (iii) | (ii) | (ii) |
During the propagation of electromagnetic waves in a medium:
| 1. | Electric energy density is half of the magnetic energy density |
| 2. | Electric energy density is equal to the magnetic energy density |
| 3. | Both electric and magnetic energy densities are zero |
| 4. | Electric energy density is double of the magnetic energy density |
A red LED emits light at \(0.1\) watt uniformly around it. The amplitude of the electric field of the light at a distance of \(1~\text{m}\) from the diode is:
1. \(1.73~\text{V/m}\)
2. \(2.45~\text{V/m}\)
3. \(5.48~\text{V/m}\)
4. \(7.75~\text{V/m}\)
| 1. | \(\begin{aligned} & \vec{B}(x, t)=\left(9 \times 10^{-8}~\text T\right) \hat{j} \sin \left[1.5 \times 10^{-6} x-2 \times 10^{14} t\right] \end{aligned}\) |
| 2. | \(\begin{aligned} & \vec{B}(x, t)=\left(9 \times 10^{-8}~\text{T}\right) \hat{i} \sin \left[2 \pi\left(1.5 \times 10^{-8} x-2 \times 10^{14} t\right)\right] \end{aligned}\) |
| 3. | \(\begin{aligned} & \vec{B}(x, t)=\left(9 \times 10^{-8}~\text{T}\right) \hat{{k}} \sin \left[2 \pi\left(1.5 \times 10^{-6}{x}-2 \times 10^{14}{t}\right)\right] \end{aligned}\) |
| 4. | \(\begin{aligned} & \vec{B}(x, t)=\left(3 \times 10^{-8}~\text{T}\right) \hat{j} \sin \left[2 \pi\left(1.5 \times 10^{-8} x-2 \times 10^{14} t\right)\right] \end{aligned}\) |
1. \({(2 \hat{i}+3 \hat{j})}\) and \({(\hat{i}+2 \hat{j})}\)
2. \({(-2 \hat{i}-3 \hat{j})}\) and \({(3\hat{i}-2 \hat{j})}\)
3. \({(3 \hat{i}+4 \hat{j})}\) and \({(4\hat{i}-3 \hat{j})}\)
4. \({(\hat{i}+2 \hat{j})}\) and \({(2\hat{i}-\hat{j})}\)
Arrange the following electromagnetic radiations per quantum in the order of increasing energy:
| A : | Blue light |
| B : | Yellow light |
| C : | X-ray |
| D : | Radiowave |
| 1. | D, B, A, C |
| 2. | A, B, D, C |
| 3. | C, A, B, D |
| 4. | B, A, D, C |
(where \(c\) is the speed of light)
1. \(\vec E=\frac{B_0}{c}\sin (kx+\omega t)\hat k~\text{V/m}\)
2. \(\vec E=-B_0c\sin (kx+\omega t)\hat k~\text{V/m}\)
3. \(\vec E=B_0c\sin (kx+\omega t)\hat k~\text{V/m}\)
4. \(\vec E=B_0c\sin (kx+\omega t)\hat k~\text{V/m}\)
Its magnetic field \(\vec B\) is given by:
1. \(\dfrac{2~E_0}{c}~\hat j\cos kz\cos \omega t\)
2. \(\dfrac{2~E_0}{c}~\hat j\sin kz\cos \omega t\)
3. \(\dfrac{2~E_0}{c}~\hat j\sin kz\sin \omega t\)
4. \(-\dfrac{2~E_0}{c}~\hat j\sin kz \sin \omega t\)
An EM wave from air enters a medium. The electric fields are \(\overrightarrow{{E}}_1={E}_{01} \hat{{x}} \cos \left[2 \pi {\nu}\left(\frac{{z}}{{c}}-{t}\right)\right] \) in air and \(\overrightarrow{{E}}_2={E}_{02} \hat{{x}} \cos {k}(2 {z}-{ct})]\) in medium, where the wave number \(k\) and frequency \(\nu\) refer to their values in air. The medium is non-magnetic. If \(\epsilon_{r_1}\) and \(\epsilon_{r_2}\) refer to relative permittivities of air and medium respectively, which of the following options is correct?
1. \( \frac{\epsilon_{r_1}}{\epsilon_{r_2}}=4 \)
2. \( \frac{\epsilon_{r_1}}{\epsilon_{r_2}}=2 \)
3. \( \frac{\epsilon_{r_1}}{\epsilon_{r_2}}=\frac{1}{4} \)
4. \( \frac{\epsilon_{r_1}}{\epsilon_{r_2}}=\frac{1}{2}\)
| 1. | \(\frac{E_0}{C}\bigg(\frac{\hat{i}-\hat{j}}{\sqrt2}\bigg) \cos\bigg[ 10^4 \frac{(\hat{i}-\hat{j})}{\sqrt2}.\overrightarrow{r} - (3 \times10 ^{12})t \bigg]\) |
| 2. | \(\frac{E_0}{C}\hat{k}\cos\bigg[ 10^4 \frac{(\hat{i}+\hat{j})}{\sqrt2}.\overrightarrow{r} +(3 \times10 ^{12})t \bigg]\) |
| 3. | \(\frac{E_0}{C}\bigg(\frac{\hat{i}-\hat{j}}{\sqrt2}\bigg)\cos\bigg[ 10^4 \frac{(\hat{i}+\hat{j})}{\sqrt2}.\overrightarrow{r} + (3 \times10 ^{12})t \bigg]\) |
| 4. | \(\frac{E_0}{C}\bigg(\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt3}\bigg)\cos\bigg[ 10^4 \frac{(\hat{i}+\hat{j})}{\sqrt2}.\overrightarrow{r} + (3 \times10 ^{12})t \bigg]\) |
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