A totally absorbing surface having an area of 7.7 cm2 faces a small source of si

Question

A totally absorbing surface having an area of 7.7 cm2 faces a small source of sinusoidal electromagnetic radiation that is 2.4 m away. At the surface. the electric field amplitude of the radiation is 84 V/m. (c = 3.00 times 10^8 m/s, mu_0 = 4pi times 10^-7 T middot m/A, epsilon0 = 8.85 times 10^-12 C^2/N m^2) (a) What is the radiation pressure exerted on the surface? (b) What is the total power output of the source, if it is assumed to radiate uniformly in all directions? A A laser beam has a wavelength of 633 nm and a power of 0.500 mW spread uniformly over a circle 1.20 min in diameter. This beam falls perpendicularly on a perfectly reflecting piece of paper having twice the diameter of the laser beam und a mass of 1.50 mg. (c = 3 00 times 10^8 m/s. mu0 = 4pi times 10^-7 T middot m/A, epsilon0 = 8.85 times 10^-12 C^2/N middot m^2) (a) What are the amplitudes of the electric and magnetic fields in this laser beam? (b) What acceleration does the laser beam give to the paper"?

Explanation / Answer

Radiation pressure due to total absorption is Pr = I/c

where I is intensity and c is speed of light = 3*10^8m/s

here I = Power/area = 0.5 eo E^2

I = 0.5 * 8.85 *10^-12 * 84* 84

I = 3.12 *10^-8 W/m^2

so

Pr = 3.12*10^-8/(3*10^8)

Pr = 1.04 *10^-16 Pa

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Total Power = I A   

P = 3.12 *10^-8 * 7.7 *10^-4

P = 2.4*10^-11 Watts

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#7:

I = power/area = 0.5 eo E^2

E^2 = 2 *Power/(area * e0)

E^2 = 2 * 0.5*10^-3 /(4*3.14*0.6*10^-3* 0.6*10^-3 * 8.85 *10^-12)

E = 5*10^6 V/m

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Electric field and magnectic field are related by

E/B = c

magnetic field B = E/c

B = 5*10^6/3*10^8

B = 16.67 mT

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