chapter24双语讲义

PROBLEMS 24-1 Maxwell’s Equations

1. Gauss ’ laws for electric fields and for magnetic fields differ due to the lack of magnetic charges. Assume that magnetic monopoles (magnetic charges) exist; denote them by the symbol M . Rewrite Gauss ’ law for magnetic fields, and give the SI units for M .

2. Equations 24-1 through 24-4 apply in a vacuum. Write Maxwell ’s equations for matter instead by using the dielectric constant εr and the relative permeability μr .

24-3 Properties of Electromagnetic Waves

3. A plane electromagnetic wave has a maximum electric field of 3.20⨯10-4 V/m. Find the maximum magnetic field.

4. If the electric field for a plane electromagnetic wave is given by E x = 0, E y = E 0 cos (kz +ωt ), and E z = 0, what are B and the direction of propagation of the wave?

5. The electric field of a certain plane electromagnetic wave is given by E x = 0, E y = 0, and .cos[()],15z E 2010t-x/c π= with c = 3.0⨯108 m/s and all quantities in SI units. Write expressions for the components of the magnetic field of the wave.

6. A plane electromagnetic wave of wavelength 1.2 m propagates in the z -direction. The electric field points in the y -direction and has amplitude of 3.0 V/m. Write an expression for the magnetic field, including its amplitude in SI units. Assume that the electric field is at its maximum at z = 0, t = 0.

24-4 Energy Transport and the Poynting V ector

7. A radio station emits a signal with a power of 50 kW. What are the amplitudes of the electric field and magnetic field at distances of 10 km and 1000 km? Assume that the signal far from the antenna is transmitted with equal intensity in all directions. (Real radio stations cannot afford to transmit their energy in this way, and their antennas distribute energy with a high degree of directionality.)

8. The electric field for a given electromagnetic wave has a peak value 50 mV/m. What is the intensity of the wave?

9. Assume that a 100 W light bulb emits light equally in all directions. What are the peak values of the electric and magnetic fields at a distance of 1 m?

10. A laser delivers 103 J of energy in a pulse that lasts 10-9 s. What are the peak electric and magnetic fields for a laser beam of diameter 10-3 m?

11. What is the intensity of a plane traveling electromagnetic wave if B m is 1.0⨯10-4 T?

12. The maximum electric field at a distance of 10 m from an isotropic point light source is 2.0 V/m. What are (a) the maximum value of the magnetic field and (b) the average intensity of the light there? (c) What is the power of the source?

13. An airplane flying at a distance of 10 km from a radio transmitter receives a signal of intensity 10 μW/m 2. Calculate (a) the amplitude of the electric field at the airplane due to this signal, (b) the amplitude of the magnetic field at the airplane, and (c) the total power of the transmitter, assuming the transmitter to radiate uniformly in all directions.

24-5 Radiation Pressure

14. A plane electromagnetic wave of wavelength 12 μm and an electric field amplitude of 10 V/m impinges on a totally reflecting surface of area 10 cm 2. What is the radiation pressure