Hollow Metal Cylinder - Physics - Exam Paper, Exams of Physics

Download Hollow Metal Cylinder - Physics - Exam Paper and more Exams Physics in PDF only on Docsity! 5 Question 1. (Marks 15) The figure shows a cross-section through a long, straight wire with radius r1 and charge per unit length λ. Co-axial with the wire is a hollow metal cylinder with internal radius r2 , external radius r3 , and a net charge per unit length 2λ. Use Gauss’s law and appropriate Gaussian surfaces to find: (a) where the charges are distributed, and the charge per unit length on each surface, (b) the electric field at a distance r < r1 from the axis, (c) the electric field at a distance r1 < r < r2 from the axis, (d) the electric field at a distance r2 < r < r3 from the axis, (e) the electric field at a distance r > r3 from the axis, and finally (f ) plot the electric field as a function of radius from the axis, from r = 0 to r > r3. Question 2. [Marks 15] Suppose you have two 3000 F capacitors (initially uncharged) and a 120 V battery. (a) Calculate the total energy stored in both capacitors if they are connected in series across the battery. Draw a schematic diagram showing how the capacitors are connected to the battery. (b) Calculate the total energy stored in both capacitors if they are connected in parallel across the battery. Draw a schematic diagram showing how the capacitors are connected to the battery. (c) Now, charge both capacitors to 120 V, then join their two +ve terminals together, and then connect their free -ve terminals across the battery. Draw a schematic diagram showing how the capacitors are connected to the battery, and the voltages on all the components just prior to the final connection being made. After the final connection is made, the capacitors will be in series with the battery, and current will flow until a new equilibrium is reached. Calculate the final voltage across each capacitor, and the total energy stored in both capacitors. 6 Question 3. (Marks 15) A conducting rod of length  = 0.50 m is free to slide on two parallel conducting rails as shown in the figure. Two resistors are connected across the rails as shown. A constant magnetic field Bin = 0.85 T is directed perpendicularly into the page as shown. The conducting rod moves to the left at a constant velocity v = 4.0 m/s due to the action of an external force. Question 2. Suppose you have two 3000F capacitors (initially uncharged) and a 120V battery. a) Calculate the total energy stored in both capacitors if they are connected in se- ries across the battery. Draw a schematic diagram showing how the capacitors are connected to the battery. b) Calculate the total energy stored in both capacitors if they are connected in paral- lel across the battery. Draw a schematic diagram showing how the capacitors are connected to the battery. c) Now, charge both capacitors to 120V, then join their two +ve terminals together, and then connect their free -ve terminals across the battery. Draw a schematic diagram showing how the capacitors are connected to the battery, and the voltages on all the components just prior to the final connection being made. After the final connection is made, the capacitors will be in series with the battery, and current will flow until a new equilibrium is reached. Calculate the final voltage across each capacitor, and the total energy stored in both capacitors. Question 3. A conducting rod of length l = 0.50 m is free to slide on two parallel conducting rails as shown in the figure. Two resistors are connected across the rails as shown. A constant magnetic field B = 0.85 T is directed perpendicularly into the page as shown. The con- ducting rod moves to the left at a co stant velocity v = 4.0 m/s due to he action of an external force. a) Calculate the current flow in each resistor. (a) Calculate the current flow in each resistor. (b) Find the total power dissipated in the two resistors. (c) Find the magnitude and direction of the applied external force that is required to maintain the velocity of the conducting rod. Question 4. (Marks 16) (a) Consider a laser that emits sinusoidal electromagnetic (EM) waves that travel in the negative x-direction. EM waves of wavelength ! " =10,600 nm are emitted from the laser into a vacuum with the E field parallel to the z-axis; the E field amplitude is ! 1.5x106 Vm"1. Write vector equations for E and B as a function of time and position. (10 marks) (b) In a CD ROM drive, light from a semiconductor diode laser having wavelength λ = 780 nm travels a distance ! 125 nm in a polycarbonate layer. Polycarbonate is a transparent medium of refractive index 1.58. Calculate, (i) the optical path length (3 marks) (ii) the wavelength of the light in the transparent medium (3 marks)