5. In free space, infinite planes y = 4 and y = 8 carry charges 20 nC/m² and 30 nC/m², re- spectively. If plane y = 2 is grounded, calculate E at P(0, 0, 0) and Q(-4, 6, 2).

2. Electromagnetic Fields and Waves (a) A charge q is moving at velocity through uniform electric and magnetic fields, E and B. The electric field and magnetic field are per- pendicular to each other and to the velocity of the charge. Write down an expression for the total force on the charge and hence determine an expression for the velocity of the charge for the case where the magnitude of the total force is zero. (b) Two charges of tq and q lie at (-1,0) and (z,0), respectively. Determine an expression for the electric field a distance y along the y-axis. (c) Unpolarised light of intensity I passes through a pair of linear polarisers. The axis of the first polariser is at 0 degrees to the vertical. After the second polariser, the intensity of light is zero. i. Use Malus' law to determine the angle that the axis of the second polariser makes with the vertical. ii. A further linear polariser is inserted between the original two polarisers. The intensity of light passing through all three polarisers is now Io/8. Determine the angle of the axis of the new polariser with respect to the vertical.

1. Oscillations and Waves (a) Explain what oscillations are and, separately, what a wave is (b) Explain the distinction between longitudinal and transverse waves. (c) You are given the following expression for the position of an oscillating body: z(t) = A(1) cos wt where is the time variable. i. If A(t) = A and are constant in time, what kind of oscillatory motion is described by z(t)? What would represent in such a case? Give its explicit expression as a function of the elastic constant & and the mass of the oscillator. ii. If A(t) = Act, with > 0, 4 and constant in time, what kind of oscillatory motion is described by z(t)? What would w represent in such a case? Give its explicit expression with re- spect to μ, k and m. (d) A travelling harmonic wave may be described by the equation: where the position, the time and all quantities, including the con- stants , and y, are in SI units. For this wave, write down each of the following physical quantities - in terms of one or more of a, 3 and Y- and briefly explain its meaning: i. The amplitude. ii. The wavelength. Specify its Sl units. iii. The frequency. Specify its SI units. iv. The speed. Specify its Sl units.

Part 4. The Ring Launcher This portion of the lab is typically done hands-on, but because we are limited in our choice of hands-on experiments right now, please watch use this URL: https://www.youtube.com/watch?v=GOSTOcyhcFM (also available as an external link on Canvas). The URL takes to a video by James Lincoln, in which he essentially recreates our laboratory experiment, almost exactly. 10) Use the ring launcher to launch several rings. 11) Why does the ring launcher NOT launch the ring with a slit in it? 12) Describe the difference between launching a copper ring and an aluminum/steel ring. 13) Describe what happens if the light bulb assembly is used instead of a ring. Why does it happen? 14) The following are top views of the copper ring in the iron core. The diagrams assume the copper ring is a single loop of wire. Magnetic field that is described for each case is in the iron core. For each of the four drawings, draw the direction (CW or CCW) of the induced current in the ring. Also indicate the direction of the magnetic field produced by this induced current.

Part 3. Anti-Gravity? This portion of the lab is typically done hands-on, but because we are limited in our choice of hands-on experiments right now, please watch use this URL: https://www.youtube.com/watch?v=N7tli71-AjA (also available as an external link on Canvas). The URL takes to a video by TSG Physics, in which the person essentially recreates our laboratory experiment, almost exactly. 7) Drop a small iron ball down the section of copper pipe. Is the motion of the ball impeded in any way? Explain. 8) Now drop the magnetic ball of the same size down the section of copper tube. Currents are induced in the tube both above and below the falling magnet (pictured here as a disc for clarity). On the drawing below, find the direction of the induced current, the direction of the induced magnetic field, and the N/S poles for both induced currents. Explain how these induced currents slow down the falling magnet. 9) Repeat for the case where the N pole of the falling magnet is below its S pole.

Part 2: Transformers In a few sentences, answer the following questions, based on what you learned in class. You may need to look some things up in a textbook or online. 3) What happens if you pass electric current through a coiled conductive wire? What if you add an iron core? 4) What effect can be observed if you bring a magnetic field near a coil of conductive wire? 5) How can you combine the above effects to use one coil to create a current in a second coil? 6) For each drawing, indicate direction of change of flux through the secondary coil, direction of induced magnetic field (in the secondary coil), and direction of induced current.

Problem 1 Two media are separated by a planar boundary which is marked as xy plane. Both media are perfect and nonmagnetic dielectrics with a dielectric constant €r1 = 2.25 in medium 1 and 2 = 4 in medium 2. In medium 1 there is a plane wave with its electric field described as E¹ = 28 cos (67 × 108 t - 30m z) (V/m) The field is a traveling wave in medium 1. It is incident on the boundary, indicated by the super index. 1. Make a sketch to show the media, the boundary, the field E¹, the associated field H', the direction of the wave propagation, and the wave front. 2. Find the phase difference in radians per meter between two wave fronts of this propagating wave in medium 1. 3. Find the time-domain expression of the field H¹. 4. Find the impedance of medium 1 and that of medium 2. Use them to compute the reflection coefficient I and the transmission coefficient 7. 5. Find the time-domain expressions of the fields of the reflected wave and the fields of the transmitted wave. You may use phasors to do the com- putation. Add to the sketch to indicate the direction of the fields of the reflected and transmitted waves and the direction they propagate. 6. Determine the time-average power densities of the incident, reflected, and transmitted waves.

Problem 3 - Review of surface integral and definition of flux. 5 pts. Consider a Cartesian co-ordinate system (x,y,z). A B-field of 2Fax+ay+2a: exists in a rectangular plane bounded by the points (0,1,1),(0,1,2).(2,0,.2).(2,0,1). The order of the points defines the direction of the winding. How much flux is traveling through the rectangular plane as a signed number.

10.1. Consider a pair of concentric spherical conductors. The inner sphere is of radius a and contains a uniformly-distributed charge Q; the larger sphere is grounded and of inner radius c. The space between the conductors is filled with two non-conducting, charge-free dielectrics, of permittivity & (a <R<b) and &2 (b<R<c). (a) Use Gauss' Laws to determine the displacement field D in the space between the conductors. (b) Find the electric field E in the two dielectric media. (c) Determine the potential difference Vo between the conductors. (d) Determine the surface charge densities ps on the surfaces of the conductors.

1. A phonograph record of radius R, carrying a uniform surface charge s, is rotating at constant angular velocity w. Find its magnetic dipole moment.