Question

Two plates, one black (perfectly absorbing) and one mirrored (perfectly reflecting), are affixed one at each end of a 9 cm rod, which is then suspended at its center from a torsion balance (see figure below). The plates are squares whose sides are of length 0.5 cm. A point light source is then placed at a distance 5 m away from the rod, as shown below. The point light source radiates an average power of 41 kW. The torsion balance keeps the rod from tinning by counteracting any torque on the rod. Assume: The direction of the EM waves are nearly perpendicular to each plate's surface (i.e., a distance 5 m from each plate), the light is radiated isotropically from the source, and uniformly distributed over the surface of each plate. What is the magnitude of the torque exerted on the torsion balance by the rod? Answer in units of N m^2.

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Answer 1

Intensity of light at the plate is, I = P/4 pi R^2 = 41 kW/4 pi(5 m)^2 = 130.6 W/m^2 = 131 W/m^2 The relation between intensity and force is, F = LA/c F = (130.6 W/m^2)(0.5 times 0.5 times 10^-4 m^2)/3.0 times 10^8 m/s F = 1.088 times 10^-11 N The torque acting on the mirrored surface is, tau = (0.45 times 10^-2 m)F tau = (0.45 times 10^-2 m)(1.088 times 10^-11 N) tau = 4.89 times 10^-14 N.m