Radiation Pressure — Question 7

Question 7

Heating and force together recover two opposing beam powers

Two vacuum beams of powers P+ and P- arrive from opposite sides of a stationary black plate. The + beam travels along +x. The measured heating rate is 9.0 W and force is 1.00 times 10 to the minus eighth N in +x. Ignore reradiation momentum and use c=3.00 times 10 to the eighth m/s.

1. Express the measured heating and force in terms of the two powers.

2. Infer both powers and give the consistency inequality any such measurements must obey.

Question 7 - Solution

Heating and force together recover two opposing beam powers

(a) Method and calculation

$$\dot Q=P_++P_-,\quad cF_x=P_+-P_-.$$$$\boxed{P_\pm=(\dot Q\pm cF_x)/2}.$$

(b) Interpretation and further calculation

$$cF_x=3.00\,\mathrm W\Rightarrow\boxed{P_+=6.00\,\mathrm W,\quad P_-=3.00\,\mathrm W}.$$$$P_\pm\ge0\Rightarrow\boxed{|cF_x|\le\dot Q}.$$

Physical check

Heating adds the two energy inputs, whereas signed momentum transfer subtracts them.