PHYS 211 Final, Fall 2007

Physics 211 Final Exam January 28, 2008 Your name: ID number: Time given: 120 minutes Please provide your reasoning for each step of your solution (providing an answer without a solution is not enough) 1 Problem 1 A uniformly charged insulating shell has internal and external radii R and 3R and the volume charge density is ρ. The points A and B are located at the inner and outer surfaces of the shell, as shown on the Figure 1. Find the potential difference ∆VAB = VB − VA. 2 Problem 2 An electric circuit consists of the 3 batteries with the voltages ∆V1 = 1V ,∆V2 = 4V and ∆V3 = 8V and 3 resistors R1 = 3Ω, R2 = 2Ω and R3 = 8Ω, as shown on the Figure 2. Find the electric currents in each of the resistors. 3 Problem 3 In the circuit shown on the Figure 3, two capacitors with capacitances C1 = C and C2 = 4C are originally disconnected, as shown on the Figure 3, and the capacitor C1 carries the charge Q while the charge of C2 is 3Q. Then the keys A and B are switched on simultaneously. Find the total heat dissipated in the resistor R after the switches A and B are on. 4 Problem 4 Two point charges q1 = 10−4C and q2 = 10−3C are separated by the distance d = 10−2m along the x-axis and move with velocities vecv1 = 2⃗i + 3⃗j( m s ) and ⃗v2 = 3⃗i + 4⃗j( m s ) respectively. Find the magnetic interaction force between two charges. 5 Problem 5 A conductor with the cylindrical cross-secrion of the radius R carries the radially symmetric current density j(r) = αr2; r ≤ R where α is a given constant (the current is into the page). Find the magnetic field as the function of the distance from the conductor’s symmetry axis, both inside and outside the conductor. 6 Problem 6 A rectangular contour , consisting of the resistor R and two conducting rods ( each of them having the same resistance 2R) is placed in a uniform magnetic field B (into the page) , perpendicular to the plane of the contour. The rods move with velocities v and 3v respectively, as shown on the Figure 6. Find the magnitude and the direction of the current in the resistor R. 7