Question

Estimate the radiation pressure due to a bulb that emits 25 W of EM radiation at a distance of 7.0 cm from the center of the bulb. Assume that light is completely absorbed.

Estimate the force exerted on a fingertip at this point. Suppose that the area of the fingertip is 1.3 cm2 . Assume that light is completely absorbed.

Answer 1

Energy absorbed per 1m² of the surface at radius R ..
E = W / (4πR²) .. .. ..(J/s) per m² ----- (1)

The mass equivalent of this energy .. M = E/c² (Einstein) .

. so ..

M = W / (4πR² c²) .. (kg/s) per m² ----- (2)

For an absorbing area, A (m²) .. equ (2) becomes .. A.W / (4πR² c²) .. kg/s---- (3)

From Newton L2 .. F = rate of change of momentum of absorbed mass (m/t x v)
F = M (kg/s ) x c .. .. F = A.W / (4πR² c) ---- (4)

Radiation pressure .. p = F/A .. .. p = W / (4πR² c) ----- (5)

a) Using .. p = 25 / (4π [0.07m]² x 3.0*10 ^8) .. .. ..P =1.35*10^(-6) N/m²

b) F = p x area .. 1.35*10^(-6) N/m² x (1.3^-4 m²) .. .. F = 1.759*10^(-10) N