Assume the mostly infrared radiation from a heat lamp acts like a continuous wav

Question

Assume the mostly infrared radiation from a heat lamp acts like a continuous wave with wavelength 1.50 µm.

(a) If the lamp's 195 W output is focused on a person's shoulder, over a circular area 24.0 cm in diameter, what is the intensity? kW/m2

(b) What is the peak electric field strength? kV/m

(c) Find the peak magnetic field strength. µT (d) How long will it take to increase the temperature of the 4.00 kg shoulder by 2.00°C, assuming no other heat transfer and given its specific heat is 0.830 kcal/kg·°C? s

Explanation / Answer

a> Intensity = Power / area = 195/ (pi * (diameter/2)2 = 195/(3.14*0.12*0.12) = 4312.6 W/m2

b> power density/speed of light = 0 * E2    <=> 4312.6 / (3 * 10^8) = 8.85 × 10-12 * E2

E = 1274.5 V/m = 1.274 KV/m

c> E/B = c hence B = E/c = 1274.5/(3*10^8) = 4.25 µT

d> Energy required = Specific heat* mass * (change in temperature) = 0.830*4*2 = 6.64 Kcal = 27781.76 Joules

Energy = power * time   <=> 27781.76 = 195* time <=> time = 142.47 sec

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