A circular uniform laser beam has a power of P = 4.9 mW and a diameter of d = 4.

Question

A circular uniform laser beam has a power of P = 4.9 mW and a diameter of d = 4.5 mm. The beam is a form of electromagnetic radiation with both electric (E0) and magnetic (B0) field components. (a)The power if the laser beam is P = 4.9 mW and it is spread uniformly over a circular cross section d = 4.5 mm in diameter. Calculate the intensity (I) of the beam in units of W / m2. (b)The laser beam is incident on a material that completely absorbs the radiation. For a laser power of P = 4.9 mW, how much energy (U) is delivered to the material in a time interval of t = 0.405 s. Express the energy in units of Joules. (c)Use the intensity of the beam (I) to calculate the amplitude of the electric field E0 in units of V / m. (d)The amplitudes of the electric and magnetic fields in an electromagnetic wave have a fixed relationship. Based on that relationship, use the result in Part (c) to calculate the amplitude of the magnetic field (B0) in units of Tesla.

Explanation / Answer

a) Intensity I = P / A

P = 4.9 mW = 4.9 * 10-3 W, A = pi * d2 /4 = 1.59 * 10-5 m2

I = 4.9 * 10-3 / 1.59 * 10-5= 308.1 W/m2

b) energy transferred = power * t = 4.9 * 10-3 * 0.405 = 1.98 * 10-3 J

c) Relation between Erms and intensity 1/2 I = 1/2 * e0 * Erms2 c

1/2 * 308.1 = 1/2 * 8.854 * 10-12 * Erms2 * 3 * 108

Erms = 340.58 V/m

E0 = sqrt 2 * Erms= 481.65 V/ m

d) Relation between amplitude of electric and magnetic field E = c B

B = E / c = 481.65 / 3 * 108

= 1.60 * 10-6 T

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