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This is second of our many quizzes on Electromagnetic waves. Click on this to access more such competitive quizzes on Current Electricity and EMI.

Electromagnetic waves Quiz 2

physics

The maxima and minima of electric field and magnetic field of electromagnetic waves, 

EM waves are transverse waves and the electric field and magnetic field are in phase with each other and both reach their maxima and minima at the same points in space i.e. their maxima and minima coincide. 

  In an isotropic, homogeneous and lossless media electromagnetic waves are transverse waves and the electric field and magnetic field are mutually perpendicular to each other and they are in phase with each other and both reach their maxima and minima at the same points in space i.e. their maxima and minima coincide.

Which graph shows the correct plot of the relative wavelength of electromagnetic waves of three colors of light, Blue light, Green light, Red light ? 

 In the electromagnetic spectrum, the wavelength of the different colors of the visible light region in ascending order is; Violet < Indigo < Blue < Green < Yellow < Orange < Red. The one with smaller wavelength will have their crest closer to each other than that of the ones with larger wavelength. 

  &nbsp;<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/8854a731-41f5-4c0f-b925-50a217e51dbe3379439919337065418.png"/>$\\$ In the electromagnetic spectrum, the wavelength of the different colors of the visible light region $(\lambda =400nm-700nm)$ in ascending order is as follows; Violet < Indigo < Blue < Green < Yellow < Orange < Red. So, the wavelength graph is; Blue < Green < Red. The color with smaller wavelength will have their crest closer to each other than that of the color with larger wavelength and vice versa.

If an electromagnetic wave is travelling in a medium with a speed of $0.33\,c$, where $c$ is speed of light and the magnitude of its electric field is $825$ W/m, what will be the magnitude of its magnetic field? 

The relationship between the magnitudes of electric field and magnetic field of electromagnetic wave travelling in vacuum is given by ${{B}_{0}}=\dfrac{{{E}_{0}}}{c}$. Put the values given in the question and find the magnitude of the magnetic field vector. 

 The relationship between the magnitudes of electric field and magnetic field of electromagnetic wave travelling in vacuum is given by, $\\ {{B}_{0}}=\dfrac{{{E}_{0}}}{c} \\ $ According to the question, $ \\ {{E}_{0}}=825\,W/m\,\text{and}\,c=3\times {{10}^{8}}\,m/s \\ $ Putting the above values in equation, we get, $ \\ \therefore{{B}_{0}}=2.75\times {{10}^{-6}}\,T$

 If the peak electric field is $98$ V/m, then the intensity of the electromagnetic wave is 

 The intensity of an electromagnetic wave is given by $I=\dfrac{1}{2}c{{\in }_{0}}{{E}_{0}}^{2}$.Put the values given in the question and find the intensity of an electromagnetic wave. 

 The intensity of an electromagnetic wave is given by, $ \\ I=\dfrac{1}{2}c{{\in }_{0}}{{E}_{0}}^{2} \\ $ According to the question, $ \\ {{E}_{0}}=98\,V/m,{{\in }_{0}}=8.85\times {{10}^{-12}}\,C/N{{m}^{2}}\,\text{ and }\,c=3\times {{10}^{8}}\,m/s \\ $ Putting the above values in equation, we get, $\\ \therefore I=12.7\,W/{{m}^{2}}$

How are the intensity, electric and magnetic field of an electromagnetic wave propagating in space at the speed of $3\times {{10}^{8}}m/s$ related to the square of the distance from the source? 

 The intensity of an electromagnetic wave is given by $I=\dfrac{P}{A}=\dfrac{P}{4\pi {{r}^{2}}}$    and $I=\dfrac{1}{2}c{{\in }_{0}}{{E}_{0}}^{2}$. Hence, intensity is inversely proportional to square of the distance and electric and magnetic fields are inversely proportional to distance from the source. 

The intensity of an electromagnetic wave is given by, $ \\ I=\dfrac{P}{A}=\dfrac{P}{4\pi {{r}^{2}}}….(i) \\ $ And intensity is also given by given by, $ \\ I=\dfrac{1}{2}c{{\in }_{0}}{{E}_{0}}^{2}….(ii) \\ $ From equation $(i)$ and $(ii)$ it is evident that, $ \\ I\propto \dfrac{1}{{{r}^{2}}} \\ \Rightarrow I\propto {{E}_{0}}^{2}\propto {{B}_{0}}^{2} \\ \therefore {{E}_{0}}\propto \dfrac{1}{r},{{B}_{0}}\propto \dfrac{1}{r} \\ $ So, intensity is inversely proportional to square of the distance and electric and magnetic fields are inversely proportional to distance from the source.