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When you look at the North Star (Polaris), you intercept ligllt from a star at a distance of 431 ly and emitting energy at a rate of 2.2 xx10^(3) times that of our Sun (P_("sun" ) = 3.90xx10^(26) W. Neglecting any atmospheric absorption, find the ans values of the electric and magnetic fields when the starlight reaches you. |
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Answer» Solution :(1) The rms value `E_(rms)`of the electric field in light is related 10 the intensity I of the light via Eq. 32-28 `(I= E_("rms")^(2) //cmu_(0))` . (2) Because the source is so far away and emits light with equal intensity in all directions, the intensity lat any distance r from the source is related to the source.s power `P_(x) ` via Eq. 32-29 `(I=P_(3)//4pir^(2)`). (3)The magnitudes of the electric field and MAGNETIC lleld of an electromagnetic wave at any instant and al any point in the wave are related by the speed of Light c ACCORDING to Eq. 32-5 (E/B = c). Thus, therms values of those fields are also related by Eq. 32-5. Electric field: Putting the first two ideas together gives us `I = (P_(s))/(4pir^(2))=(E_("rms")^(2))/(cmu_(0))` `E_("rms")= sqrt((P_(s)cmu_(0))/(4pir^(2)))` By substituting `P_(s)= (2.2xx10^(3))(3.90xx10^(26)W)` r= 431 1y= `4.08xx10^(18)`m and values for the constants we find `E_("rms") = 1.24xx10^(-3) V//m~~1.2 m ` V/m . ( Answer) Magnetic field : From Eq . 32-5 we wirte `B_(rms) = (E_(rms))/(c ) = (1.24xx10^(-3)V//m)/(3.00xx10^(8)m//s)` . Cannot compare the fields: Note that `E_(rms)`(= 1.2 mV/m) is smaJl as JUDGED by ordinary LABORATORY standards, but `B_(rms)(=4.1P T)` , (= 4.1 pT) is quite smalJ. This difference helps to explain why most instruments used for the detection and measurement of electromagnetic waves are designed to respond to the electric component. It is wrong, however, to say that the electric component of an electromagnetic wave is "stronger" than the magnetic component. You cannot compare quantities that are measured in different units. However, these electric and magnetic components are on an equal basis because their average energies, which can be compared, are equal. |
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