1. The figure shows two long parallel wires carrying currents I 1 = 15 A and I 2 = 32 A (notice the currents run in opposite directions).

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1 Final Eam Physics 222 7/29/211 NAME Use o = C 2 /N.m 2, o = N.m 2 /C 2, o/= 1-7 T m/a There are additional formulas in the final page of this eam. 1. The figure shows two long parallel wires carrying currents I 1 = 15 A and I 2 = 32 A (notice the currents run in opposite directions). Y 45 o P 45 o X I 1 I 2 d = 5.3 cm 1.A Use the diagram aboe to draw (approimately to scale). The ector magnetic field at P due to the current I 1. The ector magnetic field at P due to the current I 2. The net magnetic field ector at P due to both currents. Note: P is the origin of the system of coordinates. 1. The magnitude of the net magnetic field at P is equal to (in units of T) a) 47 b).4 c) 19d) 16 e) NA 2. 2.A A certain wire has a resistance R. What is the resistance of a second wire, made of the same material, that is half as long and has half the diameter. a) (1/2)R b) 4 c) 2Rd) (1/4) R e) NA

2 2. The figure shows a wire carrying current. The wire has three sections with different radii. 2R o R o 1.5 R o P U Rank the sections according to the following quantities (greatest first): Magnitude of the current density: > U >P Magnitude of electric field: > U >P 3. The figure shows a top-iew and a side-iew of a rectangular current loop PUT in a uniform magnetic field. The dimension of the sides of the loop are 5.4 cm and 8.5 cm. The current circulating in the loop is I= 15 ma P I T TOP VIEW U Rotation ais IDE VIEW 3.A In both diagrams aboe, draw the ector forces acting on each of the 4 sides of the loop.

3 3. The loop is placed in a configuration shown in the figure below Calculate the magnetic torque acting on the loop (in units of 1-3 A m 2 ) a).12 b) 1.72 c) 81d) e) NA 4. A parallel plate capacitor is 5% filled with a dielectric of dielectric constant = 2.5, while the remaining olume is empty (see figure below.) The area of the plates is A= 3 cm 2 and the separation distance between the parallel plates is d = 3.5 mm. After charging the capacitor with a 14 Volts battery, the battery is disconnected. P ide d iew 4A The capacitance of the capacitor is equal to (in units of 1-12 F) a) 1.3 b).2 c) 27 d) 61 e) NA 4 The figure aboe also shows a couple of point P and where we want to ealuate the corresponding electric filed. Which of the following epression(s) is(are) correct? a) The magnitude of the electric field at P is greater than at b) The magnitude of the electric field at P is weaker than at c) The magnitude of the electric field at is equal to N/C d) The electric field magnitude at P is equal to 1 4 N/C

4 e) All the epressions aboe are incorrect 5. A square loop of wire PUT with side a = 2 cm and resistance R=1 Ohms carries an current I 2 =3 ma. The loop is placed near an infinitely long wire carrying current I 1 = 1 ma, as shown in the figure. The distance from the long wire to the center of the loop is also a. U a a P I 2 T I 1 5A Calculate the magnitude of the net force (in Newtons) acting on the square loop: a) b) c) d) e) NA 5 Calculate the magnitude of the force acting on the segment P (in units of 1-12 Newtons) a) 2.1 b) 6.6 c) 8 d) e) NA 6. A positie point charge q = 1 C is located at the center of a spherical metal shell of inner radius R=2 cm. and thickness t =.3R. The net charge of the shell is Q shell = -2C. (This does not take into account the charge at the center of the shell)..3r R q = 1 C 6A ketch the charge distribution eerywhere in or on the shell AND indicate:

5 Total charge on the inner wall = -1 C Total charge inside the bulk of the shell = Total charge on the outer wall = -1 C 6 The electric field at a point P located 3 cm from the center is equal to (in units of 1 6 N/C) a) 25 b) 1 c) 49 d) 4 e) NA 7 7A The figure at the right shows portions of two large, parallel, non-conducting sheets, each with a fied uniform charge. The surface charge densities are 1 =12 C/m 2 and 3 = 12 C/m 2, respectiely. The separation between the plates is.5 mm. The Electric potential difference between the plates is equal to (in units of 1 3 V) a) 4.4 b) 14 c) d).67 e) NA 7 The figure at the right shows portions of two large, parallel, non-conducting sheets, each with a fied uniform charge. The surface charge densities are 1 =12 C/m 2 and 4 = - 12 C/m 2, respectiely. The separation between the plates is.5 mm The Electric potential difference between the plates is equal to (in units of 1 6 V) a) 4.4 b) 14 c) d).67 e) NA

6 8. 8A The figure shows two perspectie iews of the same magnet moing away from a circular metal loop. N N. On the right side figure: Indicate, using the conentional notation and, the induced current that circulates along the loop. Draw also the magnetic field lines established by the induced current, indicating eplicitly the direction of those lines. 8 The figure shows two perspectie iews of the same magnet approaching a circular metal loop. N. N On the right side figure: Indicate, using the conentional notation and, the induced current that circulates along the loop. Draw also the magnetic field lines established by the induced current, indicating eplicitly the direction of those lines. 9. The figure shows the cross section of a family of parallel equipotential surfaces and three paths along which we (as an eternal agent) shall moe an electron from one surface to another (at constant elocity). P - 4 V -2 V V 2 V 4 V 6V U

7 9A Use the graph aboe to draw the electric field lines eerywhere in between the surfaces 9 The eternal work done in each case (P,, U) is, respectiely a),, b),, - c) -, -, - d) -, -, e) NA ONU 1 (3 points) A capacitor is charged with a 2V battery. The battery remains connected. ubsequently, an eternal agent (not shown in the figure) increases the distance between the plates. 2V - E i Q i d i 2V - E f Q f df -Q i At t= At t > -Q f Which epression describes correctly what happens as the distance between the plates is increased? a) The electric field remains constant. b) The electric potential between the plates decreases. c) The electric potential energy stored in the capacitor decreases. d) The magnitude of the charge in each plate increases. e) All the epressions aboe are incorrect. 2 (3 points) The figure shows three situations in which a positiely charged particle moes at elocity through a uniform magnetic field and eperiences a magnetic force. In each situation, determine whether the orientation of the ectors are physically reasonable.. F. F F I II III

8 a) F, F, T b) T, T, F c) F, F, T d) F, T, T e) NA ome formulas: nano ln( ab ) = ln( a ) ln ( b ) ln( a/b ) = ln( a ) - ln ( b ) Electron mass: Kg Proton mass = Kg 1 Gauss = 1-4 Tesla Centripetal acceleration: R 2 a c ELECTRICITY 1 q2 q1 Coulomb's Law: F u 2 4 r Electric field, along the z-ais, due to a charge Q distributed uniformly along a thin ring 1 Q z of radius R.: E kˆ 3 / z R For an infinite uniformly charged sheet: E = /2 o Gauss' Law = E ds = q / o, where q is the net charge inside the gaussian surface Definition of Electric Potential V ( r) W et ( q q r) Electric potential due to a point charge q: V 1 4 q r Relationship between E and V: E = - dv/d About capacitance Q = C V C = A o /d U = CV 2 / 2 = Q 2 / 2 C RC circuit: Time constant = RC MAGNETIM F = q F = force, q= charge, = elocity, = magnetic field Magnetic field produced by a charge q that moes with elocity

9 q 3 4 r r = L i = Magnetic flu, L = inductance, i = current Hall effect I = nqtv Hall Inductie reactance X L = L I 4 1 R I 4 R Magnetic field at the center of a semi-circle of radius "R" Magnetic field at the center of an arc of angle f (in radians) and radius "R". I 2 r Magnetic field produced by a infinitely long wire at a distance "r" from it. F L I a I b 2 d Force per unit length between two parallel long wires, carrying currents Ia and Ib respectiely, separated by a distance "d" Faraday's Law, t where = Magnetic flu and = electromotie force Definition of the magnetic dipole moment of a loop of area A, carrying a current I: = I A n where A = area, I current, n = unit ector perpendicular to the loop