SCS 139 Applied Physic II Semester 2/2011

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1 SCS 139 Applied Physic II Semester 2/2011 Practice Questions for Magnetic Forces and Fields (I) 1. (a) What is the minimum magnetic field needed to exert a N force on an electron moving at m/s? (b) What magnetic field strength would be required if the field were 45 to the electron s velocity? Ans: (a) 1.6 mt; (b) 2.27 mt 2. What is the magnitude of the magnetic force on a proton moving at m/s (a) at right angle; (b) at 30 ; (c) parallel to a magnetic field of 0.50 T? Ans: (a) N; (b) N; (c) 0 N 3. A magnetic field of 0.10 T points in the positive x direction. A charged particle carrying 1.0 μc enters the field region moving at 20 m/s. What are the magnitude and direction of the force on the particle when it first enters the field if it does so moving (a) in the positive x direction; (b) in the positive y direction; (c) in the positive z direction; (d) at 45 to both positive x and positive y axes? Ans: (a) 0 N; (b) N, -z; (c) N, +y; (d) N, -z 4. Moving in the x direction, a particle carrying 1.0 μc experiences no force. Moving with speed v at 30 to the x axis, the particle experiences a magnetic force of 2.0 N. What magnetic force would it experience if it moved along the y axis with speed v? Ans: 4 N 5. A beam of electrons moving in the positive x direction at m/s enters a region where a uniform magnetic field of 180 G points in the positive y direction. The mass of an electron is kg. How far into the field region does the beam penetrate? Ans: 2.75 mm 6. How long does it take an electron to complete a circular orbit at right angles to a 1.0 G magnetic field? The mass of an electron is kg. Ans: s 7. What is the magnitude of the force on a 50 cm long wire carrying 15 A at right angles to a 500 G magnetic field? Ans: N 8. In a high-magnetic field experiment, a conducting bar carrying 7.5 ka passes through a 30 cm long region containing a 22 T magnetic field. If the bar makes a 60 angle with the field direction, what force is necessary to hold it in place? Ans: N 9. A piece of wire with mass per unit length 75 g/m runs horizontally at right angles to a horizontal magnetic field. A 6.2 A current in the wire results in its being suspended against gravity. What is the magnetic field strength? Ans: T

Additional Questions for Magnetic Forces and

[Halliday, Resnick, and Walker, 9E, P28.

93 10 9 s 2. 24] Ans: (a) 1.11 10 7 m/s; (b) 3.

43] Ans: (a) 0; (b) 0.138 N; (c) 0.138 N; (d) 0

2 Additional Questions for Magnetic Forces and Fields (I) 1. [Halliday, Resnick, and Walker, 9E, P28.18] Ans: (a) m/s; (b) m; (c) s 2. [Halliday, Resnick, and Walker, 9E, P28.24] Ans: (a) m/s; (b) m. 3. [Halliday, Resnick, and Walker, 9E, P28.42] Ans: (a) 16 ˆj N; (b) 0 4. [Halliday, Resnick, and Walker, 9E, P28.43] Ans: (a) 0; (b) N; (c) N; (d) 0

3 SCS 139 Applied Physic II Semester 2/2011 Practice Questions for Magnetic Forces and Fields (II) 1. [HRW, 9E, P29.1] A surveyor is using a magnetic compass 6.1 m below a power line in which there is a steady current of 100 A. (a) What is the magnetic field at the site of the compass due to the power line? (b) Will this field interfere seriously with the compass reading? The horizontal component of Earth s magnetic field at the site is 20 mt. Ans: (a) 3.3 T (b) yes 2. [YFF, 2011, E28.3] A long, straight conductor carries a 1.0 A current. At what distance from the axis of the conductor does the resulting magnetic field have magnitude B = T (about that of the earth s magnetic field in Pittsburgh)? Ans: 4 mm 3. [HRW, 9E, P29.9] Two long straight wires are parallel and 8.0 cm apart. They are to carry equal currents such that the magnetic field at a point halfway between them has magnitude 300 mt. (a) Should the currents be in the same or opposite directions? (b) How much current is needed? Ans: (a) opposite (antiparallel) (b) 30 A 4. [HRW, 9E, P29.7] In Figure 1, two circular arcs have radii a = 13.5 cm and b = 10.7 cm, subtend angle = 74.0, carry current i = A, and share the same center of curvature P. What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at P? Figure 1: [HRW, 9E, Fig ] Ans: (a) T (b) out of the page 5. [HRW, 9E, P29.8] In Figure 2, two semicircular arcs have radii R 2 = 7.80 cm and R 1 = 3.15 cm, carry current i = A, and share the same center of curvature C. What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at C? Figure 2: [HRW, 9E, Fig ]

4 Ans: (a) 1.67 T (b) into the page 6. [HRW, 9E, P29.10] In Figure 3, a wire forms a semicircle of radius R = 9.26 cm and two (radial) straight segments each of length L = 13.1 cm. The wire carries current i = 34.8 ma. What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at the semicircle s center of curvature C? Figure 3: [HRW, 9E, Fig ] Ans: (a) T (b) into the page 7. [HRW, 9E, P29.11] In Figure 4, two long straight wires are perpendicular to the page and separated by distance d 1 = 0.75 cm. Wire 1 carries 6.5 A into the page. What are the (a) magnitude and (b) direction (into or out of the page) of the current in wire 2 if the net magnetic field due to the two currents is zero at point P located at distance d 2 = 1.50 cm from wire 2? Ans: (a) 4.3 A (b) out Figure 4: [HRW, 9E, Fig ]

5 Additional Questions for Magnetic Forces and Fields (II) 1. [HRW, 9E, Q29.1] Error! Reference source not found. shows three circuits, each consisting of two radial lengths and two concentric circular arcs, one of radius r and the other of radius R > r. The circuits have the same current through them and the same angle between the two radial lengths. Rank the circuits according to the magnitude of the net magnetic field at the center, greatest first. Figure 5: [HRW, 9E, Fig ] Ans: c > a > b 2. [HRW, 9E, P29.21] Figure 6 shows two very long straight wires (in cross section) that each carry a current of 4.00 A directly out of the page. Distance d 1 = 6.00 m and distance d 2 = 4.00 m. What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to the wires? Figure 6: [HRW, 9E, Fig ] Ans: T 3. [HRW, 9E, P29.44] Figure 7 shows two closed paths wrapped around two conducting loops carrying currents i 1 = 5.0 A and i 2 = 3.0 A. What is the value of the integral for (a) path 1 and (b) path 2? Ans: (a) T m (b) T m Figure 7: [HRW, 9E, Fig ]

SCS 139 Applied Physic II Semester 2/2011 Practice Questions for Magnetic Forces and Fields (II) 1. [HRW, 9E, P29.45] Each of the eight conductors in Figure 1 carries 2.

6 SCS 139 Applied Physic II Semester 2/2011 Practice Questions for Magnetic Forces and Fields (II) 1. [HRW, 9E, P29.45] Each of the eight conductors in Figure 1 carries 2.0 A of current into or out of the page. Two paths are indicated for the line integral integral for (a) path 1 and (b) path 2? B ds. What is the value of the Path 1 Path 2 Figure 1: [HRW, 9E, Fig ] Ans: (a) 2.5 T m (b) 0 2. [HRW, 9E, P29.50] A solenoid that is 95.0 cm long has a radius of 2.00 cm and a winding of 1200 turns; it carries a current of 3.60 A. Calculate the magnitude of the magnetic field inside the solenoid. Ans: 5.7 mt 3. [HRW, 9E, P29.51] A 200-turn solenoid having a length of 25 cm and a diameter of 10 cm carries a current of 0.29 A. Calculate the magnitude of the magnetic field B inside the solenoid. Ans: T Practice Questions for Induction and Inductance 4. [HRW, 9E, P30.7] In Figure 2: [HRW, 9E, Fig ], the magnetic flux through the loop 2 increases according to the relation B 6.0t 7.0t, where B is in milliwebers and t is in seconds. (a) What is the magnitude of the emf induced in the loop when t = 2.0 s? (b) Is the direction of the current through R to the right or left? Ans: (a) 31 mv (b) to the left Figure 2: [HRW, 9E, Fig ]

7 5. A conducting loop with area 0.15 m 2 and resistance 6.0 lies in the x-y plane. A patially uniform magnetic field points in the +z direction. The field varies with time according to B t at b where a = 2.0 T/s 2 and b = 8.0 T. Find the magnitude of the loop current (a) z 2 when t = 3.0 s and (b) when B z = 0 T. Ans: (a) 0.3 A (b) 0.2 A 6. The magnetic field inside a 20 cm diameter solenoid is increasing at the rate of 2.4 T/s. How many turns should a coil wrapped around the outside of the solenoid have in order that the emf induced in the coil is 15V. Ans: 199 turns 7. A circular wire loop 40 cm in diameter has 100 resistance and lies ina horizontal plane. A uniform magnetic field points vertically downward, and in 25 ms, it increases linearly from 5 mt to 55 mt. Find the magnetic flux through the loop at (a) the beginning and (b) the end of the 25 ms period. (s) What is the loop current during this time? Ans: (a) Wb (b) Wb (c) 2.5 ma

8 Additional Questions for Magnetic Forces and Fields (II) 8. [HRW, 9E, P29.58a] Figure 3a shows a length of wire carrying a current i and bent into a circular coil of one turn. In Figure 3b the same length of wire has been bent to give a coil of two turns, each of half the original radius. (a) If B a and B b are the magnitudes of the magnetic fields at the centers of the two coils, what is the ratio B b /B a? Figure 3: [HRW, 9E, Fig ] Ans: 4 9. [HRW, 9E, P29.56] Figure 4 shows an arrangement known as a Helmholtz coil. It consists of two circular coaxial coils, each of 200 turns and radius R = 25.0 cm, separated by a distance s = R. The two coils carry equal currents i = 12.2 ma in the same direction. Find the magnitude of the net magnetic field at P, midway between the coils. Ans: 8.78 T Figure 4: [HRW, 9E, Fig ]

9 SCS 139 Applied Physic II Semester 2/2011 Practice Questions for Induction and Inductance 1. [HRW, 9E, P30.40] The inductance of a closely packed coil of 400 turns is 8.0 mh. Calculate the magnetic flux through the coil when the current is 5.0 ma. Ans: 10-7 Wb 2. [HRW, 9E, P30.44] A 12 H inductor carries a current of 2.0 A. At what rate must the current be changed to produce a 60 V emf in the inductor? Ans: -5 A/s 3. [HRW, 9E, P30.45] At a given instant the current and self-induced emf in an inductor are directed as indicated in Figure 1. (a) Is the current increasing or decreasing? (b) The induced emf is 17 V, and the rate of change of the current is 25 ka/s; find the inductance. Figure 1: [HRW, 9E, Fig ] Ans: (a) decreasing (b) H. 4. A conducting loop of area 240 cm 2 and resistance 12 lies at right angles to a spatially uniform magnetic field. The loop carries an induced current of 320 ma. At what rate is the magnetic field changing? Ans: 160 T/s 5. A 60 ma current is flowing in a 100 mh inductor. Over a period of 1.0 ms the current is reversed, going steadily to 60 ma in the opposite direction. What is the inductor emf during this time? Ans: 12V i t 3t 15t 8 i t 2 6. The current in a 2.0 H inductor is given by where t is in seconds and is in amperes. Find an expression for the magnitude of the inductor emf. Ans: 12t+30 V 7. [Modified from HRW, 9E, P30.53] A solenoid having an inductance of 6.30 H is connected in series with a 1.20 k resistor. A 14.0 V battery is connected across the pair as shown in Figure 2. Suppose, at time t 0 = 0 s, the current i through the resistor is 0 A. Figure 2: [HRW, 9E, Fig ] a. A long time later ( t ), what is the value of i. b. Find the inductive time constant L.

10 Additional Practice Questions for Induction and Inductance 8. [Modified from HRW, 9E, P30.53] (Continued from Q7) A solenoid having an inductance of 6.30 H is connected in series with a 1.20 k resistor. A 14.0 V battery is connected across the pair as shown in Figure 2. Suppose, at time t 0 = 0 s, the current i through the resistor is 0 A. a. Find the current i at an arbitrary time t > 0 s. (This will be a function of t.) b. Find the current i at time t = s. c. Find the time at which the current through the resistor reaches 80.0% of its final value. d. What is the current through the resistor at time t = t 0 + L? 8 Ans: (1) 11.7 ma; (b) 5.25 ns; (c) t i t e 7.38 ma. ma; (d) 2.0 ma; (e) 8.45 ns; (f) 9. [HRW, 9E, P30.91] In the circuit of Figure 3, R 1 = 20 k, R 2 = 20 k, L = 50 mh, and the ideal battery has = 40 V. Switch S has been open for a long time when it is closed at time t = 0. Just after the switch is closed, what are (a) the current i bat through the battery and (b) the rate di bat /dt? At t = 3.0 s, what are (c) i bat and (d) di bat /dt? A long time later, what are (e) i bat and (f) di bat /dt? Figure 3: [HRW, 9E, Fig ] Ans: (a) 0; (b) 800 A/s; (c) 1.8 A; (d) 439 A/s; (e) 4mA; (f) [HRW, 9E, P30.95] In Figure 4, R 1 = 8.0, R 2 = 10, L 1 = 0.30 H, L 2 = 0.20 H, and the ideal battery has = 6.0 V. (a) Just after switch S is closed, at what rate is the current in inductor 1 changing? (b) When the circuit is in the steady state, what is the current in inductor 1? Ans: (a) 20 A/s; (b) 0.75 A Figure 4: [HRW, 9E, Fig ]

11 HRW, 9E, P30.91 Friday, February 22, :52 AM Part 2.II Page 1

12 Part 2.II Page 2

13 Part 2.II Page 3

14 SCS 139 Applied Physic II Semester 2/2011 Practice Questions for Alternating Current 1. [HRW, 9E, P31.28] A 1.50 F capacitor is connected as in Figure 1 to an ac generator with amplitude m = 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is (a) 1.00 khz and (b) 8.00 khz?. Figure 1: A capacitor is connected across an alternating-current generator. [HRW, 9E, Fig ] Ans: (a) A; (b) A 2. [HRW, 9E, P31.29] A 50.0 mh inductor is connected as in Fig to an ac generator with amplitude m = 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is (a) 1.00 khz and (b) 8.00 khz?. Figure 2: An inductor is connected across an alternating-current generator. [HRW, 9E, Fig ] Ans: (a) 95 ma; (b) 12 ma 3. [HRW, 9E, P31.30] A 50.0 resistor is connected as in Fig to an ac generator amplitude m = 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is (a) 1.00 khz and (b) 8.00 khz?. Figure 3: A resistor is connected across an alternating-current generator. [HRW, 9E, Fig. 31-8] Ans: (a) 0.6 A; (b) 0.6 A 4. [HRW, 9E, P31.31] (a) At what frequency would a 6.0 mh inductor and a 10 F capacitor have the same reactance? (b) What would the reactance be? Ans: (a) 650 Hz; (b) 24.5

15 Practice Questions for Maxwell Eqns and EM Wave 5. [HRW, 9E, P32.1] The magnetic flux through each of five faces of a die (singular of dice ) is given by B N Wb, where N (= 1 to 5) is the number of spots on the face. The flux is positive (outward) for N even and negative (inward) for N odd. What is the flux through the sixth face of the die? Ans: +3 Wb 6. [HRW, 9E, P32.2] Figure shows a closed surface. Along the flat top face, which has a radius of 2.0 cm, a perpendicular magnetic field B of magnitude 0.30 T is directed outward. Along the flat bottom face, a magnetic flux of 0.70 mwb is directed outward. What are the (a) magnitude and (b) direction (inward or outward) of the magnetic flux through the curved part of the surface? Figure 4: [HRW, 9E, Fig ] Ans: (a) 1.1 mwb; (b) inward 7. [HRW, 9E, P33.10] A plane electromagnetic wave has a maximum electric field magnitude of V/m. Find the magnetic field amplitude. Ans: T 8. [HRW, 9E, P33.11] A plane electromagnetic wave traveling in the positive direction of an x axis in vacuum has components Ex = Ey = 0 and Ez = (2.0 V/m) cos[( s -1 )(t - x/c)]. (a) What is the amplitude of the magnetic field component? (b) Parallel to which axis does the magnetic field oscillate? (c) When the electric field component is in the positive direction of the z axis at a certain point P, what is the direction of the magnetic field component there? Ans: (a) T; (b) y; (c) -y

Question 1. Question 2

Question 1. Question 2 Question 1 Figure 29-26 shows cross sections of two long straight wires; the left-hand wire carries current i 1 directly out of the page. The net magnetic field due to the two currents is to be zero at