scs 139 applied physic ii semester 2/2011 - t u - 2 - all - practice.pdf · scs 139 applied physic...

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 5.410-15

N force on an electron

moving at 2.1107 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 2.5105

m/s (a) at right

angle; (b) at 30°; (c) parallel to a magnetic field of 0.50 T?

Ans: (a) 210-14

N; (b) 110-14

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) 210-6

N, -z; (c) 210-6

N, +y; (d) 1.410-6

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 8.7106 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 9.1010-31

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 9.1010-31

kg.

Ans: 3.5710-7

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: 0.375 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: 4.29104 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: 0.119 T

Additional Questions for “Magnetic Forces and Fields (I)”

1. [Halliday, Resnick, and Walker, 9E, P28.18]

Ans: (a) 4.9910

6 m/s; (b) 0.00710 m; (c) 8.9310

–9 s


Ans: (a) 1.1110

7 m/s; (b) 3.1610

-4 m.


Ans: (a) ˆ16 j N; (b) 0


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


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 = 0.510-4

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 = 0.411 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. 29-38]

Ans: (a) 1.0310-7

T (b) out of the page

5. [HRW, 9E, P29.8] In Figure 2, two semicircular arcs have radii R2 = 7.80 cm and R1 = 3.15

cm, carry current i = 0.281 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?


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?


Ans: (a) 1.1810-7

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 d1 = 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 d2 = 1.50 cm from

wire 2?


Ans: (a) 4.3 A (b) out

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.


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 d1= 6.00 m and distance d2 = 4.00

m. What is the magnitude of the net magnetic field at point P, which lies on a perpendicular

bisector to the wires?


Ans: 2.5610-7

T

3. [HRW, 9E, P29.44] Figure 7 shows two closed paths wrapped around two conducting loops

carrying currents i1 = 5.0 A and i2 = 3.0 A. What is the value of the integral for (a) path 1 and

(b) path 2?


Ans: (a) -2.510-6

Tm (b) -1.610-5

Tm


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 B ds . What is the value of the

integral for (a) path 1 and (b) path 2?


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: 2.910-4

T

Practice Questions for “Induction and Inductance”

4. [HRW, 9E, P30.7] In Figure 2: [HRW, 9E, Fig. 30-36], the magnetic flux through the loop

increases according to the relation 26.0 7.0B t t , 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

Path 1 Path 2

5. A conducting loop with area 0.15 m2 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

2

zB t at b where a = 2.0 T/s2 and b = 8.0 T. Find the magnitude of the loop current (a)

when t = 3.0 s and (b) when Bz = 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) 6.2810-4

Wb (b) 0.0069 Wb (c) 2.5 mA

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 Ba and Bb are the magnitudes of the

magnetic fields at the centers of the two coils, what is the ratio Bb/Ba?


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


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.


Ans: (a) decreasing (b) 6.810-4

H.

4. A conducting loop of area 240 cm2 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

6. The current in a 2.0 H inductor is given by 23 15 8i t t t where t is in seconds and i t

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 t0 = 0 s, the current i through the resistor is 0 A.


a. A long time later ( t ), what is the value of i.

b. Find the inductive time constant L .

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 t0 = 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 = 0.000000001 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 = t0 + L ?

Ans: (1) 11.7 mA; (b) 5.25 ns; (c) 81.9 1011.7 1 ti t e mA; (d) 2.0 mA; (e) 8.45 ns; (f)

7.38 mA.

9. [HRW, 9E, P30.91] In the circuit of Figure 3, R1= 20 k, R2= 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 ibat through the battery and (b) the

rate dibat/dt? At t = 3.0 s, what are (c) ibat and (d) dibat/dt? A long time later, what are (e) ibat

and (f) dibat/dt?


Ans: (a) 0; (b) 800 A/s; (c) 1.8 A; (d) 439 A/s; (e) 4mA; (f) 0

10. [HRW, 9E, P30.95] In Figure 4, R1= 8.0 , R2= 10 , L1= 0.30 H, L2 = 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

HRW, 9E, P30.91Friday, February 22, 2013 8:52 AM

Part 2.II Page 1

Part 2.II Page 2

Part 2.II Page 3


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. 31-10]

Ans: (a) 0.283 A; (b) 2.262 A

2. [HRW, 9E, P31.29] A 50.0 mH inductor is connected as in Fig. 31-12 to an ac generator with



Figure 2: An inductor is connected across an alternating-current generator. [HRW, 9E, Fig. 31-12]

Ans: (a) 95 mA; (b) 12 mA

3. [HRW, 9E, P31.30] A 50.0 resistor is connected as in Fig. 31-8 to an ac generator



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

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 32-26 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?


Ans: (a) 1.1 mWb; (b) inward

7. [HRW, 9E, P33.10] A plane electromagnetic wave has a maximum electric field magnitude

of 3.2010-4 V/m. Find the magnetic field amplitude.

Ans: 1.0710-12 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[(1015 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) 6.710-9 T; (b) y; (c) -y

scs 139 applied physic ii semester 2/2011 - t u - 2 - all - practice.pdf · scs 139 applied physic...

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