A heat lamp emits infrared radiation whose rms electric field is Erms = 2744 N/C

Question

A heat lamp emits infrared radiation whose rms electric field is Erms = 2744 N/C. (a) What is the average intensity of the radiation? W/m2 (b) The radiation is focused on a person's leg over a circular area of radius 4.1 cm. What is the average power delivered to the leg? W (c) The portion of the leg being radiated has a mass of 0.31 kg and a specific heat capacity of 3500 J/(kg · C°). How long does it take to raise its temperature by 2.3 C°? Assume that there is no other heat transfer into or out of the portion of the leg being heated.

Explanation / Answer

(a)
The Poynting vector is th representation of the energy flux density, i.e intensity of an electromagnetic wave, it is the cross product of electric field vector and magnetic field vector. For simple plane wave propagation can you can derive the time averaged magnitude of this vector as:
|S| = (1/2)cE² = cE_rms²
with
vacuum permittivity, c speed of light, E amplitude of the electric field

So the average intensity of the infrared radiation is:
|S| = 8.8542×10¹² C²N¹m² 2.9979×10 ms¹ (2744 NC¹)²
=1.9×10 Wm²


(b)
P = |S| A = |S|R²
= 1.9×10 Wm² (4.3×10² m)^2
= 110.36 W


(c)
Q/t = P
<=>
mCT/t = P
=>
t = mCT/P
= 0.31 kg 3500 Jkg¹°C¹ 2.3 °C / 110.36 Js¹
= 22.61 s

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