zgribestika

2021-12-15

The energy flow to the earth from sunlight is about $1.4{\left\{k\frac{W}{m}\right\}}^{2}$ .

(a) Find the maximum values of the electric and magnetic fields for a sinusoidal wave of this intensity.

(b) The distance from the earth to the sun is about$1.5\times {10}^{11}m$ Find the total power radiated by the sun.

(a) Find the maximum values of the electric and magnetic fields for a sinusoidal wave of this intensity.

(b) The distance from the earth to the sun is about

Vivian Soares

Beginner2021-12-16Added 36 answers

(a) The indicated value indicates the intensity $I=1.4k\frac{W}{{m}^{2}}$ of the light. An electromagnetic wave's intensity in a vacuum is inversely proportional to the amplitude of the electric field. $E}_{max$ and the amplitude of magnetic field $B}_{max$ and is given by the equation:

$I=\frac{1}{2}{\u03f5}_{0}c{E}_{max}^{2}$, where $\u03f5}_{0$ is a electric constant, $c$ is speed of light.

Now, solve the equation for $E}_{max$

$E}_{max}=\sqrt{\frac{2I}{{\u03f5}_{0}c}$

Plug the values for $I,\u03f5,c$ into equation

$E}_{max}=\sqrt{\frac{2I}{{\u03f5}_{0}c}$

$=\sqrt{\frac{2\left(1400\frac{W}{{m}^{2}}\right)}{(8.85\times {10}^{-12}\frac{{C}^{2}}{N}\times {m}^{2})(3\times {10}^{8}\frac{m}{s})}}$

Maximum magnetic field and maximum electric field have a relationship in the following way:

$B}_{max}=\frac{{E}_{max}}{c$

Now, plug the values into the equation

${B}_{max}=\frac{{E}_{max}}{c}=\frac{1026\frac{V}{m}}{3\times {10}^{8}\frac{m}{s}}=3.42\times {10}^{-6}T$

(b) The intensity is propotional to $E}_{max}^{2$ and represents the incident power $P$ per area $A$

$P=IA$

The radius of the Earth's path around the Sun is represented by the distance between it and the Sun, and this distance is thought to be a sphere. The area is computed as follows:

$A=4\pi {r}^{2}=4\pi {(1.5\times {10}^{11}m)}^{2}=2.82\times {10}^{23}{m}^{2}$

Now, plug in the values:

$P=IA=\left(1400\frac{W}{{m}^{2}}\right)(2.82\times {10}^{23}{m}^{2})=3.95\times {10}^{26}W$

The answer is: (a) $3.42\times {10}^{-6}T$, (b) $3.95\times {10}^{26}W$

22+64

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