Chapter25_HW Solutions (Das, Phys 1302)2. Picture the Problem: The figure shows the electric field in the positive y direction and the magnetic field in the positive z direction.Strategy: Use the Right-Hand Rule (RHR) to determine the direction of propagation. Point the fingers of your right hand in the direction of the electric field. Bend them in the direction of the magnetic field. Your thumb points in the direction of the wave propagation.Solution: According to the RHR, the wave is traveling in the positive x direction .Insight: If the magnetic field had been in the positive x direction with the same electric field, the wave would propagate in the negative z direction.4. Picture the Problem: A person on the positive y-axis observes an electromagnetic wave that radiates from an electric charge that oscillates sinusoidally about the origin and along the z-axis.Strategy: In order for the radiation to reach the person, it must propagate in the positive y direction (toward the person). The electric field will oscillate in the same direction as the charge. The magnetic field will oscillate perpendicular to the electric field and perpendicular to the direction of propagation.Solution: 1. (a) The electric field will oscillate in the z direction .2. (b) The magnetic field will oscillate in the x direction.3. (c) The electromagnetic wave will propagate in the positive y direction.Insight: If the person were standing on the positive x-axis, and at some instant the electric field were in the +z direction, the magnetic field would be in the −y direction, as the wave propagated in the positive x direction.6. Picture the Problem: The figure shows the direction of propagation, direction of the electric field, and/or the direction of the magnetic field for four electromagnetic waves.Strategy: For each of the waves use the Right-Hand Rule to determine the missing information. Point the fingers of your right hand in the direction of the electric field, bend them in the direction of the magnetic field, and then your thumb will point in the direction of the wave propagation. If the electric field or magnetic field is unknown, guess the direction to see if your thumb points in the correct direction of propagation.Solution: 1. (a) The magnetic field points in the +z direction.2. (b) The electric field points in the − z direction.3. (c) The magnetic field points in the – x direction.4. (d) The wave propagates in the − x direction.Insight: Because the three directions are mutually perpendicular, when two are known the third must be along the remaining axis. The RHR tells whether it is positive or negative.7. Picture the Problem: A wave propagates in the positive z direction and has a known electric field vector.Strategy: Because the magnetic field is perpendicular to the electric field, the magnitudes of the x and y components of the magnetic field are proportional to the y and x components of the electric field, respectively, with the constant of proportionality given by equation 25-9. Use the Right-Hand Rule to determine the sign of each component. Solution: 1. (a) Because B is perpendicular to the direction of propagation, the z component is zero.2. (b) Switch the components of the electric field and divide by c to calculate Bx and By: B =-Eycˆx+Excˆy3. Insert the electric field components: B =13.00 ´ 108 m/s- 2.87 N/C( )ˆx+ 6.22 N/C( )ˆyéëùû= - 9.57 ´ 10- 9 T( )ˆx+ 2.07 ´ 10- 8 T( )ˆyInsight: Calculating the magnitude of the magnetic field gives 9.57 nT( )2+ 20.7 nT( )2=22.8 nT as stated in the problem. This problem can also be solved by using the vector cross product (see Appendix A).8. Picture the Problem: A wave propagates in the positive z direction with a known magnetic field vector.Strategy: Because the magnetic field is perpendicular to the electric field, the magnitudes of the x and y components of the magnetic field are proportional to the y and x components of the electric field, respectively, with the constant of proportionality given by equation 25-9. Use the Right-Hand Rule to determine the sign of each component. Solution: 1. (a) Because E is perpendicular to the direction of propagation, the z component is zero.2. (b) Switch the components of the magnetic field and multiply by c to calculate Ex and Ey: E =c - Byˆx+Bxˆy( )3. Insert the electric field components: E = 3.00 ´ 108 m/s( )- - 5.28 ´ 10- 9 T( )ˆx+ 3.02 ´ 10- 9 T( )ˆyéëùû= 1.58 N/C( )ˆx+ 0.906 N/C( )ˆyInsight: Calculating the magnitude of the electric field gives 1.58 N/C( )2+ 0.906 N/C( )2=1.82 N/C as stated in the problem. This problem can also be solved by using the vector cross product (see Appendix A).9. Picture the Problem: The figure at the right shows three electromagnetic waves with various orientations.Strategy: The propagation direction is the same as the direction of E ´B. Use the Right-Hand Rule to determine the directions of propagation.Solution: To find the direction of propagation of an E&M wave, point the fingers of the right hand in the direction of the electric field, curl them toward the direction of the magnetic field, and your thumb will point in the direction of propagation. Applying this rule, we find the following directions of propagation: case 1, positive x direction; case 2, positive z direction; case 3, negative x direction.Insight: Likewise, if E pointed in the positive x direction and B pointed in the positive z direction, the wave would propagate in the negative y direction.20. Picture the Problem: As a motorist approaches a yellow signal light, the motorist sees the light Doppler shifted to green.Strategy: Use equation 25-4 to calculate the two frequencies from the wavelengths, and then insert the frequencies into equation 25-3 to solve for the speed.Solution: 1. (a) Calculate the frequencies: f =c l = 3.00 ´ 108 m/s( )590 ´ 10- 9 m( )=5.0847 ´ 1014 Hz¢f =c ¢l = 3.00 ´ 108 m/s( )550 ´ 10- 9 m( )=5.4545 ´ 1014 Hz2. Solve equation 25-3 for the speed: ¢f = f 1+u c( )u =c¢ff- 1æèçöø÷=3.00 ´ 108 m/s5.45 ´ 1014 Hz5.08 ´ 1014 Hz- 1æèçöø÷= 2.2 ´ 107 m/s3. (b) The wavelength decreases if the motorist travels toward the traffic light. Insight: If the motorist were traveling away from the light, it would have a wavelength of 640 nm and appear red.21. Picture the Problem: Light of frequency 5.000×1014 Hz is emitted from a galaxy that is receding from Earth at a