Exam 2 Fall 2015

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Lee Holt
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1 Exam 2 Fall 2015 Section instructor Section number Last/First name Last 3 Digits of Student ID Number: Show all work. Show all formulas used for each problem prior to substitution of numbers. Label diagrams and include appropriate units for your answers. You may use an alphanumeric calculator during the exam as long as you do not program any formulas into memory. By using an alphanumeric calculator you agree to allow us to check its memory during the exam. Simple scientific calculators are always OK! A Formula Sheet Is Attached To The Back Of This Examination Be Prepared to Show your Student ID Card Score on each problem: 1. (30) 2. (20) 3. (20) 4. (20) Total Score (out of 90 pts)

2 2 1. Conceptual Questions (30 point) Put a circle around the letter that you think is the best answer (6pts) Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively A) 1 is neutral, 2 is negative, and 3 is positive B) 1 is neutral, 2 is positive, and 3 is negative C) 1 is positive, 2 is neutral, and 3 is negative D) 1 is positive, 2 is negative, and 3 is neutral E) 1 is negative, 2 is neutral, and 3 is positive 1.2. (6pts) What is the time constant for the discharge of the capacitors shown in the figure? A) 4RC B) RC/4 C) RC D) RC/ (6pts) A loop of a square wire is positioned in the vicinity of a very long straight wire carrying an increasing current. Find the direction of the induced current in the loop. (CW stands for a clockwise direction; CCW counterclockwise) A) CW B) CCW C) No current D) None of the above

3 (6pts) The line integral of B around the loop shown in the figure is µ0 5.0 A. Current I4 is A) 0 A B) 3.0 A into the page C) 3.0 A out of the page D) 1.0 A into the page E) 1.0 A out of the page (6pts) The figure shows four long parallel wires (positioned at the corners of a square with a diagonal 2a) which carry equal currents I into and out of the page as shown. What is a value of a magnetic field at the center of the square? A) μμ 0 II/2ππππ B) μμ 0 4II/2ππππ C) μμ 0 II/ππππ D) 0

4 4 Problem 2. (20 pts) A circular loop in the plane of the paper lies in a 0.75-T magnetic field pointing into the paper. If the loop s diameter changes from 20.0 cm to 6.0 cm in 0.5 s, a) What is the direction of the induced current, b) What is the magnitude of the averaged induced EMF, c) If the coil resistance is 2.5 Ω, what is the average induced current?

5 5 Problem 3. (20 pts) A long straight cylindrical wire conductor of radius R carries a current I of uniform current density in the conductor. Determine the magnetic field due to this current at: a) Points outside the conductor (r > R), b) Points inside the conductor (r < R), c) If R = 2 mm and I = 60 A, what is B at r = 1 mm, and r = 3 mm (Show Amperian loops; at least for one of the cases (a or b) show how you handle a linear integral) Problem 4. (20 pts)

6 6 The right edge of the circuit in the figure extends into a 50 mt uniform magnetic field. a) What is the magnitude of the net force on the circuit? b) What is the direction of the net force on the circuit? Formula Sheet: Electricity and Magnetism Coulomb s law

7 7 FF = kk qqqq rr 2 Electric Field EE = FF qq Field of a point charge EE = kk QQ rr 2 Electric field inside a capacitor EE = ηη εε 0 Principle of superposition Electric flux Gauss s law NN EE nnnnnn = EE ii ii=1 Φ EE = EE ddaa Φ = EE ddaa = QQ iiii εε 0 Electric potential VV = UU qq ΔV = VV ff VV ii = EE ddss ii For a point charge VV(rr) = 1 QQ 4ππεε 0 rr For a paralle-plate capacitor VV = EEEE Potential Energy UU = qqqq Two point charges ff Capacitors UU = kk qqqq rr CC = QQ ΔVV AA Parallel-plate CC = εε 0 dd Capacitors connected in parallel CC eeee = CC 1 + CC 2 + Capacitors connected in series 1 = CC eeee CC 1 CC 2 Energy stored in a capacitor UU = QQ2 Ohm s law VV = IIII II = dddd dddd RR = ρρ ll AA II iiii = II oooooo ΔVV ii = 0 Power PP = IIII Resistors connected in series RR eeee = RR 1 + RR 2 + RR 3 + Resistors connected in parallel 1 = RR eeee RR 1 RR 2 RR 3 The potential difference across a charging capacitor in RC circuit VV(tt) = εε(1 ee tt RRRR) Discharged RC circuit 2CC

8 8 QQ = QQ 0 ee tt ττ; ττ = RRRR A magnetic field exerts a force dddd = IIdddd BB FF = IIll BB FF = qqvv BB The Biot-Savart Law BB = μμ 0qqvv rr 4ππrr 2 ddbb = μμ 0IIIIss rr 4ππrr 2 The magnetic field of: A straight line wire BB = μμ 0II 2ππππ A solenoid BB = μμ 0 nnnn Magnetic flux Inductance Φ BB = BB ddaa LL = Φ BB II LL = µ 0NN 2 AA ll εε = LL dddd dddd Energy stored in an inductor BB dddd = μμ 00 II rr cccccc = mmmm qqqq Constants Charge of an electron ee = CC Electron mass mm = kkkk Permittivity of free space εε 0 = CC 2 /NNmm 2 Permeability of free space μμ 0 = 4ππ 10 7 TTTT/AA kk = 1 = NNmm 2 /CC 2 4ππεε 0 Kinematic eq-ns with const. Acc.: v(t) = v 0x +at x(t) = x 0 + v 0x t +(1/2) at 2 v 2 2 = v 0x + 2a(x x 0 ) Centripetal acceleration aa RR = vv 2 rr L=2πR A=πR 2 V=(4/3)πR 3 UU = LL II2 2 Faraday s Law Ɛ = EE dddd = ddφφ BB dddd Ampere s Law

Exam 2 Fall 2014

1 95.144 Exam 2 Fall 2014 Section instructor Section number Last/First name Last 3 Digits of Student ID Number: Show all work. Show all formulas used for each problem prior to substitution of numbers.