a) A source of electromagnetic waves radiates power uniformly in all directions
ID: 2154466 • Letter: A
Question
a) A source of electromagnetic waves radiates power uniformly in all directions at a single frequency. At a distance of 5.00 km from the source, a detector measures the intensity of the wave to be 23.0 ?W/m2. What is the peak value of the magnetic field at the detector due to the wave?b) What is the average power radiated by the source?
c) Now the detector is replaced with a perfectly absorbing sheet normal to the incident flux, with surface area 2.30 m2. What is the force on the sheet due to the wave?
Explanation / Answer
For the average power, you can directly calculate it from the intensity given. Since you know the intensity, you know how much power you have per unit area, at the distance of 5.0 km, so multiplying that by the area will give you the total average power. The area you should use is the area of a sphere with radius 5.0 km (can you see why?). For the force on the sheet, the main concept is "conservation of momentum". Or, rather, F = dp/dt. Because EM wave carries momentum, as the sheet absorbs the EM wave, it will absorb its momentum along with it. So, all you need to do is calculate the momentum change per unit time due to the incident EM wave, and that'll give you the force. The momentum of EM wave is given by Poynting vector, and in fact, it looks like Wikipedia has a formula that you can use directly
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