Δ x = c Δ t y x z x E B B B A FIGURE 22–11 Electromagnetic wave carrying energy through area A. E and B from the Sun. Radiation from the Sun reaches the Earth (above the atmosphere) with an intensity of about Assume that this is a single EM wave, and calculate the maximum values of E and B . APPROACH We solve Eq. 22 – 8 for in terms of and use SOLUTION From Eq. 22 – 2, so NOTE Although B has a small numerical value compared to E (because of the way the different units for E and B are defined), B contributes the same energy to the wave as E does, as we saw earlier. B 0 = E 0 c = 1.01 * 10 3 V m 3.00 * 10 8 m s = 3.37 * 10 – 6 T. B = E c , = 1.01 * 10 3 V m. E 0 = C 2 I 0 c = C 2 A 1350 J s m 2 B A 8.85 * 10 – 12 C 2 N m 2 BA 3.00 * 10 8 m s B I = 1350 J s m 2 . I E 0 A I = 1 2 0 cE 0 2 B 1350 J s m 2 . 1350 W m 2 = EXAMPLE 22 ; 4 C A U T I O N E and B ha v e v ery different v alues (due to ho w units are defined), but E and B contribute equal energy
SECTION 22 – 6 635 22–6 Momentum Transfer and Radiation Pressure If electromagnetic waves carry energy, then we would expect them to also carry linear momentum. When an electromagnetic wave encounters the surface of an object, a force will be exerted on the surface as a result of the momentum trans- fer just as when a moving object strikes a surface. The force per unit area exerted by the waves is called radiation pressure , and its existence was predicted by Maxwell. He showed that if a beam of EM radiation (light, for example) is completely absorbed by an object, then the momentum transferred is c d (22 ; 9a) where is the energy absorbed by the object in a time and c is the speed of light. If, instead, the radiation is fully reflected (suppose the object is a mirror), then the momentum transferred is twice as great, just as when a ball bounces elastically off a surface: c d (22 ; 9b) If a surface absorbs some of the energy, and reflects some of it, then where a has a value between 1 and 2. Using Newton’s second law we can calculate the force and the pressure exerted by EM radiation on an object. The force F is given by The radiation pressure P (assuming full absorption) is given by (see Eq. 22 – 9a) We discussed in Section 22 – 5 that the average intensity is defined as energy per unit time per unit area: Hence the radiation pressure is (22 ; 10a) If the light is fully reflected, the radiation pressure is twice as great (Eq. 22 – 9b): (22 ; 10b) c fully reflected d P = 2 I c . c fully absorbed d P = I c . I = ¢ U A ¢ t . I P = F A = 1 A ¢ p ¢ t = 1 Ac ¢ U ¢ t . F = ¢ p ¢ t . ¢ p = a ¢ U c , radiation fully reflected ¢ p = 2 ¢ U c . ¢ t ¢ U radiation fully absorbed ¢ p = ¢ U c , (F = ¢ p ¢ t ) Solar pressure. Radiation from the Sun that reaches the Earth’s surface (after passing through the atmosphere) transports energy at a rate of about Estimate the pressure and force exerted by the Sun on your outstretched hand.
- Spring '14