physics
posted by Sarah .
An electromagnetic wave in a vacuum has a magnetic field with a magnitude of 1.7 x 10^6 T. What is the intensity S of the wave?

physics 
bobpursley
In plane waves
In a propagating sinusoidal linearly polarized electromagnetic plane wave of a fixed frequency, the Poynting vector always points in the direction of propagation while oscillating in magnitude. The timeaveraged magnitude of the Poynting vector is
\langle S \rangle = \frac{1}{2 \mu_0 c} E_0^2 = \frac{\varepsilon_0 c}{2} E_0^2,
where \ E_0 is the maximum amplitude of the electric field and \ c is the speed of light in free space. This timeaveraged value is also called the irradiance or intensity I.
[edit] Derivation
In an electromagnetic plane wave, \mathbf{E} and \mathbf{B} are always perpendicular to each other and the direction of propagation. Moreover, their amplitudes are related according to
B_0 = \frac{1}{c}E_0,
and their time and position dependences are
E\left(t,{\mathbf r}\right) = E_0\,\cos\left(\omega\,t {\mathbf k} \cdot {\mathbf r} \right),
B\left(t,{\mathbf r}\right) = B_0\,\cos\left(\omega\,t {\mathbf k} \cdot {\mathbf r} \right),
where \ \omega is the frequency of the wave and \mathbf{k} is wave vector. The timedependent and position magnitude of the Poynting vector is then
S(t) = \frac{1}{\mu_0} E_0\,B_0\,\cos^2\left(\omega t{\mathbf k} \cdot {\mathbf r}\right) = \frac{1}{\mu_0 c} E_0^2 \cos^2\left(\omega t{\mathbf k} \cdot {\mathbf r} \right) = \varepsilon_0 c E_0^2 \cos^2\left(\omega t{\mathbf k} \cdot {\mathbf r} \right).
In the last step, we used the equality \varepsilon_0\,\mu_0 = {c}^{2} . Since the time or spaceaverage of \cos^2\left(\omega\,t{\mathbf k} \cdot {\mathbf r}\right) is \textstyle\frac{1}{2}, it follows that
\left\langle S \right\rangle = \frac{\varepsilon_0 c}{2} E_0^2.
E= speedlight*B
The time averaged Poynting vector is equal to epsilonfreespace*speedlight*E^2/2
but if E= speedlight*B
S= epsilonFreespace*speedlight^3*B^2 /2
check this out: http://en.wikipedia.org/wiki/Poynting_vector
Respond to this Question
Similar Questions

Physics
Suppose that the electric field of an electromagnetic wave decreases in magnitude. Does the magnetic field increase, decrease, or remain the same? 
Physics
1)An electromagnetic wave is produced by: an accelerating charged particle or changing magnetic fields. 2)Find the period of an electromagnetic wave of wavelength 2.20 x 10^2 m. 3.00 x 10^8 * 2.20 x 10^2 = 6.60 x 10^6 s 
physics
In a given electromagnetic plane wave the maximumelectric field strength is 400 V/m. What is the maximum magnetic field strength? 
College Physics
A radio station with a power of 20 kW sends out an omnidirectional wave at 1.25 MHz. a. If the electromagnetic wave has an electric field of 0.22 V/m, what is the magnetic field amplitude? 
College Physics 2056
An electromagnetic wave strikes a 3.00cm2 section of wall perpendicularly. The rms value of the wave's magnetic field is determined to be 6.00 104 T. How long does it take for the wave to deliver 1000 J of energy to the wall? 
Physics
The electromagnetic wave that delivers a cellular phone call to a car has a magnetic field with an rms value of 1.7 × 1010 T. The wave passes perpendicularly through an open window, the area of which is 0.23 m2. How much energy does … 
Physics
A stationary particle of charge q = 1.4 108 C is placed in a laser beam (an electromagnetic wave) whose intensity is 3.5 103 W/m2. Determine the magnitudes of the (a) electric and (b) magnetic forces exerted on the charge. If the … 
Physics
The magnetic vector of a plane electromagnetic wave is described as follows: B⃗ =Bmxˆsin[13 rad/m z− 3.90e9 rad/sec t] where Bm>0. This represents the full magnetic field, so that By=Bz=0. (a) What is the wavelength … 
Physics
An electromagnetic wave in a vacuum traveling in the +x direction generated by a variable source initially has a wavelength of 2.65 x 10^4 m and a maximum electric field Emax in the +y direction of 8.20×10^−3 V/m. What are … 
physics
An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is S = 1.13 109 W/m2. What is the rms value of each of the following fields in the electromagnetic wave emitted by the laser?