1 Part I: Solve the following 10 problems 1. An electron escapes from the surface of a conducting sphere with radius 5 cm and charge -5 µC. What is the highest acceleration which the electron experiences? (2 points) F a 2. kQe R2 F 3.2 1018 ms 2 m What is the electric flux through the top face of the cube shown? The side of cube is a = 15 cm and the electric field, in N/C, is E 500iˆ 700 ˆj 200kˆ . (2 points) E . dA 500 iˆ 700 ˆj 200 kˆ kˆ dA = z top face 200 a 2 4.5 N m 2 / C y a x 1 2 3. In the figure below, the ring with radius R = 6 cm is in the x-y plane and is centered at the origin. The ring carries a uniformly distributed charge of +2 nC. An electron is released from rest along the z-axis at z = 8 cm. What is the kinetic energy of the electron, in eV, as it passes through the origin? (3 points) z R K U as Kin=0 kQ kQ K e R R2 z2 1.92 10 17 J 1 2 y x K 120 eV 4. The electric potential V in a region of space is given by V = x2 – 3 y2 + z2 where V is in volts and x, y and z are in meters. What is the magnitude of the electric field at a point with coordinates x = y = z = 1 m? (3 points) Ei V so xi E 2 x iˆ 6 y ˆj 2 z kˆ E ˆ 6 ˆj 2 kˆ 1,1,1 2 i E 2 2 6 2 2 2 N / C 6.6 N / C 2 3 5. The capacitors C1 = 3.00 µF, C2 = 6.00 µF and C3 = 4.00 µF are fully charged; the capacitor C2 has a plate charge of 18.0 µC. What is the voltage across the capacitor C3? (3 points) C1 C2 Q2 18 C V2 V1 3V and Q1 9 C C3 Q3 Q12 27 C V3 Q3 C3 6.75V 6. In the circuit below, ε1 = 24.0 V, R = 12.0 Ω and r = 4.00 Ω. What is ε2 if I1 = 3.50 A? (3 points) ε1 From upper loop 1 12 I 2 0 I 2 2 A I1 Junction rule I3 I 3 I1 I 2 I 3 1.5 A I2 R r ε2 From big loop 1 2 rI 3 0 2 18V 3 4 7. A source of emf, a 10-kΩ resistor and 8-µF capacitor are connected in series. How long does it take the energy stored in the capacitor to reach 80% of its final value? (4 points) t q C 1 e U U f t 1 e t 0.8U f U f 1 e 2 2 and t 2.25 2.25 RC 0.18 s 8. A proton enters a region of uniform magnetic field (B = 0.5 T) with an initial velocity (v = 105 m/s) which makes an angle θ = 20° with the field. What is the pitch of the helical path of the proton? (3 points) v θ B v11 v cos 20 9.4 10 4 m / s T 2m 1.3110 7 s eB and p T v11 0.012 m 4 5 9. A wire bent as shown carries current I = 20 A perpendicular to the magnetic field B = 0.3 T of a solenoid. If R = 12 cm and θ = 120°, what is the magnitude of the net magnetic force exerted on the wire? (3 points) .B R R θ I F I L' B with L' 2 R sin 60 0.208 m F 1.25 N 10. A pair of point charges q1 = 5 µC and q2 = -5 µC are moving with identical speeds v1 = v2 = 105 m/s in the directions shown. When the charges are at the locations shown what are the magnitude and direction of the net magnetic field produced at the origin? (4 points) y q1 v1 v2 0.2 m 0.4 m B1 x q2 o q1 v1 1.25 T 4 0.22 B2 o q2 v2 0.313 T 4 0.4 2 Direction for both: k̂ so Bnet 1.56 T kˆ 5 6 Part II: Conceptual Questions Tick the most appropriate answer (each question carries 1 point) 1. Point charges +4q and -2q are held in the X-Y plane as shown. A free charge Q with coordinates xo and yo is in the same plane and in equilibrium. Then y a) xo < 0 and yo = 0 b) 0 < xo < a and yo = 0 c) xo > a and yo = 0 d) yo > a and xo = 0 2. -2q +4q x a A positive charge is distributed uniformly within a non-conducting spherical object. If the magnitude of the electric field and the electric potential (with respect to infinity) at the center of the object are denoted by E and V, respectively, then a) E ≠ 0 and V = 0 b) E ≠ 0 and V > 0 c) E = 0 and V = 0 d) E = 0 and V > 0 3. Four point charges are held as shown. A, B and C are the mid points on three sides of the square and D is the center point. A charge Q can be moved with constant speed from one of these points to the other one while the net work performed is zero. These two points are A -q a) A and D b) A and C c) C and D d) D and B 4. D +q C B +q Cylindrical wires 1 and 2 shown below are made of the same material and have the same length L. If I1 = 2I2, then: a) The electric fields in wires 1 and 2 are equal. b) The current densities in wires 1 and 2 are equal. c) The charge carrier concentrations in wires 1 and 2 are equal. d) The drift velocities in wires 1 and 2 are equal. 2r r 5. -q I2 wire 2 I1 wire 1 In the single loop circuit below, source of emf S is connected to load D by wires bc and ad. The conventional current I is shown. The electric potential V around the circuit is such that: I c b a) Vb = Vc > Va = Vd . b) Vd > Va > Vb > Vc. S D c) Va = Vb = Vc = Vd. d a d) Vc > Vb > Va > Vd. 6 7 6. A current I flows from b to a through the real source of emf shown below. b a) Energy is transferred to the charge at the rate εI + rI . b) Energy is transferred from the charge at the rate εI + rI2. c) Energy is transferred to the charge at the rate εI − rI2. d) Energy is transferred from the charge at the rate εI − rI2. 2 ε r a 7. The figure shows the paths of two charged particles A and B in a mass spectrometer. The semicircular paths have radii RA and RB (RA = 2RB). The mass and charge of the particles are identical. The transit times of the particles in the mass spectrometer are denoted by tA and tB. a) tA > tB b) tA < tB c) tA = 2tB d) tA = tB 8. A B The figure shows a long wire and a rectangular loop, both carrying current I in the directions shown. The direction of the net magnetic force acting on the loop is a) Upward b) Downward c) To the right d) To the left I I 9. Currents I1, I2 and I3 carried by three wires surrounded by the closed loop C are 1 B.dl around loop C is equal to shown below. The value of the line integral 0 I3 I1 a) I1 - I2 + I3 b) -I1 + I2 - I3 I2 c) I1 + I2 + I3 C d) -I1 - I2 - I3 dl 10. A ring with radius R carries current I and produces a magnetic field 0.3 mT at its center. The same current I is passing in the wire shown below where the semicircular section has the same radius R. The magnetic field at point P, the center of the semicircular section, is y a) -0.30 mT k̂ b) +0.60 mT k̂ c) +0.15 mT k̂ d) -1.60 mT k̂ x 2R . I P 2R 7