2. If B is uniform, show that A = -(r × B), where r is the vector from the origin to the point in question. That is, check that B=V x A and VA = 0.

4. A capacitor, of capacitance C = 120 μF is charged using a battery of 24 V. The internal resistance of the battery is 100 2. Once charged, the capacitor is connected to the circuit presented in the figure below. It is known that R₂=2R₁, R3=2R2, and R3 = 40052. The value of R₂ is unknown. (a) Calculate how long it takes for the capacitor to be 99% charged and determine the initial charge on the capacitor. (b) Just after connecting the capacitor C, at time t = 0, the current through R₂ is 1A. Calculate the value of R, and the energy stored in the capacitor at t = 0. (c) The resistor network, R₁, R2, R3 and R₂, can be replaced by a single equivalent resistance. Find this equivalent resistance and hence find the time constant of the discharging circuit. (d) Find the time t, after which the electric charge on C drops by a factor of 2 and calculate the energy dissipated in the circuit in time 12. (e) Calculate the energy dissipated on R, after a very long time.

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.

Lab: Electromagnetic Induction Part 1. Faraday's Law and Lenz's Law

Using a slotted line, the following results were obtained: distance of first minimum from the load =4 cm; distance of second minimum from the load =14cm;voltage standingwave ratio =1.5.If the line is lossless and Zo 500 Ω, find the load impedance.

A particle carries a charge of -3.63 x10^-8 C has a mass of 0.179 g. The particle has an initial northward velocity of 34915 m/s. What is the magnitude of the minimum magnetic field that will balance the earth's gravitational pull on the particle?

A plane wave in air with is incident upon the planar surface of a dielectric material, with &, = 4, occupying the half space z ≤ 0. Determine 1. The polarization of the incident wave 2. The angle of incidence 3. The time-domain expressions for the reflected electric and magnetic fields 4. The time-domain expression for the transmitted electric and magnetic fields 5. The average power density carried by the wave in the dielectric medium.

A lossless transmission line of electrical length 1 = 0.352 λ is terminated in a load impedance Z₂ = (60 + 30) Ω. The output impedance Z0 = 1000 Ω.Verify your results using CD Modules 2.4 or 2.5 .Including a printout of the screen's output display.