Write the equation for the energy density of electromagnetic waves.
(N/A) The total energy density $u$ of an electromagnetic wave is the sum of the energy density due to the electric field $(u_E)$ and the energy density due to the magnetic field $(u_B)$.
The energy density due to the electric field is given by $u_E = \frac{1}{2} \epsilon_0 E^2$.
The energy density due to the magnetic field is given by $u_B = \frac{1}{2} \frac{B^2}{\mu_0}$.
Since in an electromagnetic wave,the energy is equally divided between the electric and magnetic fields $(u_E = u_B)$,the total energy density is:
$u = u_E + u_B = \frac{1}{2} \epsilon_0 E^2 + \frac{1}{2} \frac{B^2}{\mu_0}$.
Alternatively,it can be expressed as $u = \epsilon_0 E^2 = \frac{B^2}{\mu_0}$.
The energy density due to the electric field is given by $u_E = \frac{1}{2} \epsilon_0 E^2$.
The energy density due to the magnetic field is given by $u_B = \frac{1}{2} \frac{B^2}{\mu_0}$.
Since in an electromagnetic wave,the energy is equally divided between the electric and magnetic fields $(u_E = u_B)$,the total energy density is:
$u = u_E + u_B = \frac{1}{2} \epsilon_0 E^2 + \frac{1}{2} \frac{B^2}{\mu_0}$.
Alternatively,it can be expressed as $u = \epsilon_0 E^2 = \frac{B^2}{\mu_0}$.
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View SolutionThe electric field part of an electromagnetic wave in a medium is represented by:
$E_x = 0;$
$E_y = 2.5 \, \text{N/C} \cos \left[ \left( 2\pi \times 10^6 \, \text{rad/s} \right) t - \left( \pi \times 10^{-2} \, \text{rad/m} \right) x \right];$
$E_z = 0.$
The wave is:
$E_x = 0;$
$E_y = 2.5 \, \text{N/C} \cos \left[ \left( 2\pi \times 10^6 \, \text{rad/s} \right) t - \left( \pi \times 10^{-2} \, \text{rad/m} \right) x \right];$
$E_z = 0.$
The wave is:
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View SolutionIn a plane electromagnetic wave,the magnetic field is given by $\vec{B} = 3 \times 10^{-7} \sin (100 \pi x + 10^{12} t) \ T$. The wavelength of the wave is (where $x$ is in meters and $t$ is in seconds). (in $m$)
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