PHYS 211 Final, Spring 2013

Score:________ Check if solution is continued on the back. 1 PHYSICS 211 Final Spring 2012-2013 TIME: 90 minutes June 20, 2013 DO NOT OPEN THIS EXAM BEFORE YOU ARE TOLD TO BEGIN NAME________________________________________________ ID Number ________________________ Useful information ε0=8.85x10-12 C2/N.m2 µ0=4π x 10-7 Tm/A q = 1.6 × 10−19 C me= 9.1x10-31 kg mp= 1.67×10-27 kg ke=8.9875x109 Nm2/C2 Grading I II III IV V VI Total Score:________ Check if solution is continued on the back. 2 I- (22) Ampere’s law 1- (10) The magnetic field of a solenoid with length l, radius a and number of turns N is uniform when a current I flows in it. Demonstrate that B=µ0nI. 2- (4) Use the definition of inductance to show that L=µ0Vn2; what it V here? 3- (3) What is the energy per unit volume stored as a function of B? Score:________ Check if solution is continued on the back. 3 4- (5) The solenoid is turned now to make a torus with radius R, re-determine the magnetic field strength inside the torus. II- (24) Faraday’s law 1- (6) Show that, for a time varying current, that the back emf is: |E|=Ldi/dt (3) In an RL-circuit shown to the right, discuss the different forms of energy. Score:________ Check if solution is continued on the back. 4 2- (11) A bar, with length l and mass m is sliding in one direction subject to a constant force Fapp, Determine the current amplitude and direction flowing as a function of time in two different ways. 3- (4) Based on the above calculation, comment on what does Faraday’s law reflects. Score:________ Check if solution is continued on the back. 5 III- (16) Ampere and Faraday’s laws Consider a current I flowing in a long straight wire with a radius a and length l. 1. (10) Determine the magnetic field magnitude and direction for r<a and for r>a. 2. (6) Let the current increase as a function of time according to I = αt+I0, determine the amplitude and the direction of the induced potential for r<a [Hint: First determine the magnetic flux area]. Score:________ Check if solution is continued on the back. 6 IV- (20) AC Circuits We consider a circuit composed of an AC power source, supplying a current I = Imaxsin(ωt), a resistor R and an inductor L. (a)(4) Consider that the resistance alone is connected to the power supply, determine the expression of the potential difference across it. (b)(4) Consider that the inductor alone is connected to the power supply, determine the expression of the potential difference across it. (c)(6) When both R and L are put in series, determine the impedance of the circuit. Score:________ Check if solution is continued on the back. 7 (d)(2) Determine the expression of the circuit phase. (e)(4) Discuss the behavior of this circuit at low frequencies (ω→0) and for (ω→∞) and plot the current Imax vs. ω t and comment on the results. ω Imax Score:________ Check if solution is continued on the back. 8 V- (10) AC Circuits We insert a capacitor in parallel to the inductor as shown in the figure below and the AC power source produces now a potential difference ε = ε0 cos(ωt). (f)(5) What are the maximum values of IL, Ic and IR in the case where ω → 0 (g)(5) What are the maximum values of IL, Ic and IR in the case where ω → ∞ VI-(8) Write down the full four equations of Maxwell and comment with one sentence on each about what does it reflect. Score:________ Check if solution is continued on the back. 9 SCRATCH PAPER Nothing on this page will be graded