Cora lies in a tanning bed getting a tan. Assume that A_S = 0.78 m^2 of her skin

Question

Cora lies in a tanning bed getting a tan. Assume that A_S = 0.78 m^2 of her skin is exposed to the light from the ultraviolet (UV) lamps. The UV lamps produce light with an average energy density of u_T = 4.6 Times 10^-6 J/m^3. She lies in the bed for t_T = 16 minutes. A_S = 0.78 m^2 U_T = 4.6 Times 10^-6 J/m^3 t_T = 16 minutes (a) Calculate the average intensity S_T in W/m^2 of the UV light. (b) If Cora's skin absorbs 100% of the energy of the UV light, calculate how much energy U in J her skin would absorb during the time she lies in the bed. (c) Calculate the rms electric field E_T in N/C of the UV light. (d) Calculate the rms magnetic field B_T in T of the UV light. B_T =

Explanation / Answer

(A) average intensity = uT c

= (4.6 x 10^-6) (3 x 10^8)

= 1380 W/m^2

(B) U = I A T
= 1380 x 0.78 x (16 x 60 s)

= 1.033 x 10^6 J

(C) I = Erms^2 / (u0 c)

1380 = Erms^2 / ( 4pi x 10^-7 x 3 x 10^8)

Em = 721.28 N/C

(D) Brms = Erms / c

= 2.404 x 10^-6 T

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