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www.GOALias.blogspot.comPhysicsWhen the sun shines on your hand, you feel the energy beingabsorbed from the electromagnetic waves (your hands get warm).Electromagnetic waves also transfer momentum to your hand butbecause c is very large, the amount of momentum transferred is extremelysmall and you do not feel the pressure. In 1903, the American scientistsNicols and Hull succeeded in measuring radiation pressure ofvisible light and verified Eq. (8.12). It was found to be of the order of7 × 10 –6 N/m 2 . Thus, on a surface of area 10 cm 2 , the force due to radiationis only about 7 × 10 –9 N.The great technological importance of electromagnetic waves stemsfrom their capability to carry energy from one place to another. Theradio and TV signals from broadcasting stations carry energy. Lightcarries energy from the sun to the earth, thus making life possible onthe earth.Example 8.2 A plane electromagnetic wave of frequency25 MHz travels in free space along the x-direction. At a particularpoint in space and time, E = 6.3 ĵ V/m. What is B at this point?Solution Using Eq. (8.10), the magnitude of B is278EXAMPLE 8.3 EXAMPLE 8.2EB = c6.3 V/m –88 2.1 10 T= = ×3×10 m/sTo find the direction, we note that E is along y-direction and thewave propagates along x-axis. Therefore, B should be in a directionperpendicular to both x- and y-axes. Using vector algebra, E × B shouldbe along x-direction. Since, (+ ĵ ) × (+ ˆk ) = î , B is along the z-direction.Thus, B = 2.1 × 10 –8 ˆk TExample 8.3 The magnetic field in a plane electromagnetic wave isgiven by B y= 2 × 10 –7 sin (0.5×10 3 x+1.5×10 11 t) T.(a) What is the wavelength and frequency of the wave?(b) Write an expression for the electric field.Solution(a) Comparing the given equation with⎡ ⎛xt ⎞⎤B y= B 0sin ⎢2π⎜ +⎝⎟ λ T ⎠⎥⎣⎦2πWe get, λ =3 m = 1.26 cm,0.5 × 10111and = ν = ( 1.5 × 10 )/2π = 23.9 GHzT(b) E 0= B 0c = 2×10 –7 T × 3 × 10 8 m/s = 6 × 10 1 V/mThe electric field component is perpendicular to the direction ofpropagation and the direction of magnetic field. Therefore, theelectric field component along the z-axis is obtained asE z= 60 sin (0.5 × 10 3 x + 1.5 × 10 11 t) V/m