1.

a. The components of the electric field in an electromagnetic wave traveling in vacuum are described by E_x=0, E_y=0, and E_z=6.31 sin(32.5 x - t) V/m, where x is in meters and t is in seconds.

b. Calculate the frequency of the wave.

c. Calculate the wavelength of the wave.

d. Calculate the amplitude of the magnetic field of the wave.

e. Calculate the intensity of the wave.

f. Assuming that the source of this wave radiates isotropically, calculate the total power of that source if it is located 155 meters away.

2. Calculate the displacement current between the round plates of a capacitor, 5.02 cm in diameter, if the plates are spaced 1.55 mm apart and the voltage across them is changing at a rate of 123 V/s.

3.

a. A 1050 nF capacitor with circular parallel plates 1.35 cm in diameter is accumulating charge at the rate of 21.6 mC/s at some instant in time. What will be the induced magnetic field strength 11.9 cm radially outward from the center of the plates?

b. What will be the value of the field strength after the capacitor is fully charged?

4. The maximum magnetic field strength of an electromagnetic field is 4.2010^-6 T. Calculate the maximum electric field strength if the wave is traveling in a medium in which the speed of the wave is 0.83c.

5. What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of 4.2010^-4 T (about 10 times the Earth's)?

6.

a. If electric and magnetic field strengths vary sinusoidally in time, being zero at t = 0, then E = E₀ cos (2ft) and B = B₀ cos (2ft). Let f = 3.00 GHz here. When are the field strengths first zero?

b. When do they reach their most negative value?

c. How much time is needed for them to complete one cycle?

7.

a. The components of the electric field in an electromagnetic wave traveling in vacuum are described by E_x=0, E_y=0, and E_z=585 sin(k x - 1.4510¹⁰ t) V/m, where x is in meters and t is in seconds. Calculate the frequency of the wave.

b. Calculate the wavelength of the wave.

c. Calculate the amplitude of the magnetic field of the wave.

d. Calculate the intensity of the wave.