1. (2 pts) The short solenoid shown in black in the figure below has n coils of area A per unit length. Current I going through the coils gives rise to a uniform magnetic field B inside the solenoid. Imagine a gaussian surface in the shape of a large cylinder as shown in red in the figure. One end of the cylinder goes through the middle of the solenoid whereas the other side goes through a wire leading to the solenoid. a. Use Gauss' law for magnetism to determine the magnetic flux through all parts of the Gaussian surface not inside the solenoid. b. Note that the result for part (a) is independent of the radius of the Gaussian surface. Can you supply an argument (by drawing magnetic field lines) of why this might be the case? 2. (3 pts) Consider a long cylindrical copper wire with radius 1.29mm and resistivity of 1.72 x 10'8 Q-m. A of current of 15A moving from left to right along the length of the wire is uniformly distributed through the cross section of the wire. a. What is the magnitude and orientation of the (uniform) electric field in the wire? (Hint: use the relationship between current density and an electric field.) b. What is the magnitude and orientation of the magnetic field due to the current 10cm from the center of the wire? c. If the current in the wire is changing at a rate of 1000A/s, what is the rate of change of the electric field in the wire? d. What is the magnitude and orientation of the magnetic field due to the changing electric field in the wire 10cm from the center of the wire? 3. (3 pts) A uniform, coherent, monochromatic beam of visible light with wavelength 640nm and circular cross section of radius 1cm carries a total power that averages 100mW. The wave is traveling in vacuum in the z-direction as described in a right-handed coordinate system. a. What is the angular wave number of the light wave? b. What is the speed of the wave? c. What is the frequency, angular frequency, and period of the light wave? d. What are the maximum electric and magnetic fields in the wave? e. If at time t=0 the electric field at z=0 is a maximum and points in the +x direction, what is the magnitude and direction of the magnetic field at z=0 at this time? f. Write the equations that describe the dependence of the electric and magnetic fields in the wave on time and z direction. Remember that fields are vectors, so you can either specify which component you are talking about or use unit vectors. 4. (2 pts) A radio transmitter changes the voltage across an antenna (that is, the voltage difference from one end of the antenna to the other) at high frequencies so that the electric field changes direction at high frequency. Take the case where the antenna is a long vertical rod. a. When the bottom of the antenna is at lower potential than the top, what is the direction of the electric field in the antenna? b. What is the direction of the electric field when the potential in the antenna changes to the top being at the lower potential? c. Explain in words why this gives rise to waves. These waves can carry the signal to a radio receiver far away. d. For the antenna described, what are the possible directions of the resulting magnetic field. e. What are the possible directions that the resulting electromagnetic waves can travel