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Homework: Topic7: Magnetic Forces & Magnetic Fields [Chap. 19]

Explanation: Problems are divided into two groups. Numbers in parentheses,

e.g. (10) are Exercises. Relatively simple applications of basic definitions and

basic laws. These are for student practice. Numbers in brackets, e.g. [10], are

assigned problems. These are problems similar in level of difficulty to test

problems. Numbers in curly brackets, e.g. {10} are challenging problems.

Exercises:

(1) In a magnetic field directed vertically upward a particle initially moving north is deflected

toward the east. What is the sign of the charge of the particle?

Ans. positive

(2) A particle having a mass of 0.50 g carries a charge of 4.60 x 10-8 C. The particle is given aninitial horizontal velocity that is due east and has a magnitude of 6.0 x 104 m/s. What are the

magnitude and direction of the magnetic field that will keep the particle moving in the earthsgravitational field in the same horizontal eastward direction?

Ans. 1.78 T; North

(3) An electron at point A in the figure has a speed of 6.0 x 106 m/s.

Find a) the magnitude and direction of the magnetic field that will cause

the electron to follow the semicircular path from A to B.b) the time required for the electron to move from A to B.

A B

10 cm

v o

Ans. a) 6.82 x 10-4 T; into the place of the figure; b) 2.62 x 10-8 s

(4) A singly ionized 7Li ion has a mass of 1.16 x 10-26 kg. It is accelerated through a potential

difference of 500 V and then enters a region of uniform magnetic field. The magnetic field has amagnitude of 0.600 T and is perpendicular to the path of the ion. What is the radius of the ions path

in the magnetic field?

Ans. 0.0142 m

(5) In the Bainbridge mass spectrometer, suppose the magnetic field B in the velocity selector is 1.30

T, and ions having a speed of 4.00 x 106

m/s pass through undeflected. a) What is the electric fieldbetween the plates? b) If the separation of the plates is 0.50 cm, what is the potential difference

across the plates?

Ans. a) 5.20 x 106 V/m; b) 2.60 x 104 V

(6) What is the maximum torque on a rectangular coil 5.00 cm x 12.0 cm and of 600 turns whencarrying a current of 4.00 x 10-5 A in a uniform field with magnitude 0.300 T?

Ans. 4.32 x 10-5 N m

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Problems:

[1] Each of the lettered circles at the corners of the cube in

the figure represent a positive charge q moving with avelocity of magnitude v in the direction indicated. The

region in the figure is a uniform magnetic field B,parallel to

the x-axis and directed toward the right. Copy the figure,find the magnitude and direction of the force on each charge,

and show the force in your diagram.

Ans. a) qvB in z dir.; b) qvB in +y dir.; c) 0 d) 2/qvB

in y dir.; e) qvB directed midway between y axis & -z

axis.

x

y

z

a

b

c

d

e

B

[2] The magnetic field B in a certain region has magnitude

1.50 T, and its direction is that of the positive x-axis. For the

figure shown:a) What is the magnetic flux through surface abcd?

b) What is the magnetic flux through surface befc?

c) What is the magnetic flux through surface aefd?

d) What is the net flux through all five surfaces that enclosethe volume?

x

y

z

a

b

c

d

e

30 cm

40 cm

50 cm

f

30 cm

Ans. a)0.180 Wb ; b) 0 c) 0.180 Wb d) 0

[3] The electric field between the plate of the velocity selector in a Bainbridge mass spectrometer is1.20 x 105 V/m, and the magnetic field in both regions is 0.600 T. A stream of singly charged neon

atoms moves in a circular path of 0.728 m radius in the magnetic field. Determine the mass of one

neon atom and the mass number of this neon isotope.

Ans. 3.50 x 10-25 kg; 21

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[4] A wire along the x-axis carries a current of 6.00 A in the +x-direction. Calculate the force

(magnitude and direction) on a 1.00 cm section of the wire exerted by the following uniform

magnetic fields:a) B = 0.600 T, in the y direction

b) B = 0.500 T, in the +z-direction

c) B = 0.300 T, in the x-directiond) B = 0.200 T, in the xz-plane at an angle of 600 from the +x-axis and 300 from the +z-axis

Ans. a)0.0360 N; -z-direction; b) 0.0300 N; -y-direction; c) 0 d) 0.0104 N; -y-direction

[5] A circular coil of wire 8.00 cm in diameter has 12 turns and carries a current of 4.00 A. The coil

is in a region where the magnetic field is 0.600 T. a) What is the maximum torque on the coil? B)

In what position would the torque be one-half as great as in part (a)?

Ans. a) 0.145 N m; Place of coil at 600 to the field.

[6] The cube in the figure is 0.50 m on a side and is in a

uniform magnetic field of 0.300 T, Parallel to the x-axis.

The wire abcdefcarries a current of 4.00 A in the directionindicated.

a) Determine the magnitude & direction of the force

acting on segments ab, bc, cd, de, ef.b) What are the magnitude & direction of the total force

on the wire?x

y

z

a

b c

d

e

B

f

Ans. Fab = 0.60 N z-direction; Fbc = 0.60 N y-direction; Fcd= 0.849 N @ 450 above z=axis in yz-

plane; Fde = 0.60 N y-direction; Fnet = Fde

[7] The rectangular loop in the figure is pivoted about the y-axis

and carries a current of 10.0 A in the direction indicated.

a) If the loop is in a uniform magnetic field of magnitude 0.400T, parallel to the x-axis, find the magnetic torque exerted on the

loop.

b) Repeat part (a) for the case in which the field is parallel to thez-axis.

c) For each of the above cases, what magnitude torque would

there be about an axis through the center parallel to the y-axis?x

y

z

8 cm

6 cm

10 A

30 o

Ans. a) 0.0166 N m; b) 0.0096 N m; c) 0.0166 N m; 0.0096 N m