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Sever21 [200]
3 years ago
7

An electromagnetic wave with frequency 65.0Hz travels in an insulating magnetic material that has dielectric constant 3.64 and r

elative permeability 5.18 at this frequency. The electric field has amplitude 7.20×10−3V/m. What is the wavelength of the wave?
Physics
1 answer:
lakkis [162]3 years ago
8 0

Answer:

  The wavelength of the wave is 1.06\times10^6 m  

Explanation:

Lets calculate

We know an electromagnetic wave is propagating through an insulating magnetic material of dielectric constant K and relative permeability K_m ,then the speed of the wave in this dielectric medium is \nu is less than the speed of the light c and is given by a relation

               \nu=\frac{c}{\sqrt{KK_m} }  --------- 1

In case the electromagnetic  wave propagating through the insulating magnetic material , the amplitudes of electric and  magnetic fields are related as -

             E_m_a_x= \nu B_m_a_x

The magnitude of the 'time averaged value' of the pointing vector is called the intensity of the wave and is given by a relation

                       I = S_a_v

                        \frac{E_m_a_xB_m_a_x}{2K_m\mu0}----------- 3

now , we will find the speed of the propagation of an electromagnetic wave by using equation 1

\nu=\frac{c}{\sqrt{KK_m} }

Putting the values ,

   =\nu= \frac{3.00\times10^8}{\sqrt{(3.64)(5.18)} }

 =0.6908\times10^8m/s

 = 6.91\times10^7m/s

Now , using this above solution , we will find the wavelength of the wave -

     \lambda=\frac{\nu}{f}

    Putting the values from above equations -

  \frac{6.91\times10^7m/s}{65.0Hz}

        \lambda= 1.06\times10^6 m

Hence , the answer is \lambda= 1.06\times10^6 m

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