Exam 2 Fall 2014

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Britney Osborne
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1 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. 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. (20) 2. (20) 3. (20) 4. (20) Total Score (out of 80 pts)

2 2 1. Conceptual Questions (20 point) Put a circle around the letter that you think is the best answer (4pts) Two loops of wire are moving in the vicinity of a very long straight wire carrying a steady current. Find the direction of the induced current in each loop. (CW stands for clockwise direction; CCW counterclockwise) Loop A: A) CW B) CCW C) No current Loop B: A) CW B) CCW C) No current 1.2.(4pts) The three loops of wire shown in the figure are all subject to the same uniform magnetic field that does not vary with time. Loop 1 oscillates back and forth as the bob in a pendulum, loop 2 rotates about a vertical axis, and loop 3 oscillates up and down at the end of a spring. Which loop, or loops, will have an induced emf? A) Loop 1 B) Loop 2 C) Loop 3 D) Loops 1 and 3 E) Loops 2 and 3

3 (4pts) Magnetic flux depends upon A) the magnetic field B) the orientation of the area with respect to the field C) the area involved D) all of the above E) none of the above 1.4. (4pts) Figure shows a small positive charge q moving toward a long current-carrying wire. Which of the arrows labeled A to D correctly represents the direction of the magnetic force applied on the charge A) A B) B C) C D) D E) The force points in a direction perpendicular to the plane of the figure (4pts) A charged particle is injected into a uniform magnetic field such that its velocity vector is perpendicular to the magnetic field vector. Ignoring the particle's weight, the particle will A) move in a straight line B) follow a spiral path C) move along a parabolic path D) move along a hyperbolic path E) follow a circular path

4 4 Problem 2. (20 pts) Calculate the currents in each resistor. (Writing the equations (15 pts); solving them (5pts)).

5 Problem 3. (20 pts) The figure shows a cross section of a hollow cylindrical conductor of radii a and b, carrying a uniformly distributed current I (direction is out of the page).

5 5 Problem 3. (20 pts) The figure shows a cross section of a hollow cylindrical conductor of radii a and b, carrying a uniformly distributed current I (direction is out of the page). Determine the magnetic field at a distance r from the axis for: (a) (6pts) r < b; (b) (8pts) b < r <a; (c) (6pts) r>a (Show amperian loops; at least for one of the cases (a, b, or c) show how you handle a linear integral)

6 6 Problem 4. (20 pts) A conducting rod whose length is 25 cm is placed on a U-shaped metal wire that has a resistance R of 8 Ω as shown in the figure. The wire and the rod are in the plane of the paper. A constant magnetic field of strength 0.4 T is applied perpendicular and into the paper. An applied force moves the rod to the right with a constant speed of 6 m/s. (a) What is the magnitude of the induced emf in the wire? (b) What is the magnitude and direction of the induced current in the wire.

7 7 Formula Sheet: Electricity and Magnetism Coulomb s law Electric Field Field of a point charge Electric field inside a capacitor Principle of superposition Electric flux Gauss s law Φ Φ Electric potential For a point charge For a paralle-plate capacitor Potential Energy q moving through V Capacitors Parallel-plate Δ Capacitors connected in parallel Capacitors connected in series Energy stored in a capacitor Ohm s law Power Resistors connected in series Resistors connected in parallel The potential difference across a charging capacitor in RC circuit 1 A magnetic field exerts a force

8 8 The Biot-Savart Law 4 4 The magnetic field of: A straight line wire 2 A solenoid Magnetic flux Φ / Permeability of free space 4 10 / / 2 Kinematic eq-ns with const. Acc.: v(t) = v 0x +at x(t) = x 0 + v 0x t +(1/2) at 2 v 2 = v 2 0x + 2a(x x 0 ) Centripetal acceleration Self-inductance Φ Energy stored in an inductor Discharged LR circuit ; / Faraday s Law Ɛ Ampere s Law Constants Charge on electron Electron mass Permittivity of free space

Exam 2 Fall 2015

1 95.144 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.