Homework: Topic7: Explanation:

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Homework: Topic
7
:

Magnetic Forces & Magnetic Fields [Ch
ap. 1
9
]

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 an
initial horizontal v
elocity that is due east and has a magnitude of 6.0 x 10
4

m/s. What are the
magnitude and direction of the magnetic field that will keep the particle moving in the earth’s
gravitational 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 10
6

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.



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
7
Li 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 o
f uniform magnetic field. The magnetic field has a
magnitude of 0.600 T and is perpendicular to the path of the ion. What is the radius of the ion’s path
in the magnetic field?


Ans. 0.0142 m


(5) In the Bainbridge mass spectrometer, suppose the magnetic f
ield B in the velocity selector is 1.30
T, and ions having a speed of 4.00 x 10
6

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


Ans. a) 5.20 x 10
6

V/m; b) 2.60 x 10
4

V


(6) What is the maximum torque on a rectangular coil 5.00 cm x 12.0 cm and of 600 turns when
carrying 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
















Problems:


[1] Each of the lettered circles at the corners of the cube in
the figure represent a positive charge q moving with a
velocity of magnitude v in the direction indicated. The
region in the figure is a uniform magnetic field
B,
parallel to
t
he 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⁤楲⸻†戩ⁱ療⁩渠 y⁤楲⸻† ⤠〠†))

楮i

y⁤楲⸻†⁥⤠煶B

摩decte搠浩摷dy⁢ 瑷te渠

y⁡x楳…
-

ax楳i



[㉝⁔桥慧湥瑩c⁦楥汤l
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 sur
face
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 enclose
the volume?



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 is
1.20 x 10
5

V/m, and the magnetic field in both regions is 0.600 T. A stream of singly charged neon
atoms moves in a circular pat
h 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


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

d) B = 0.200 T, in the xz
-
plane at an angle of

60
0

from the +x
-
axis and 30
0

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 60
0

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
abcdef

carries a current of 4.00 A in the direction
indicated.


a) Determine the magnitude & direction of the force
acting on segments
ab, bc, cd, de, ef.


b) Wha
t are the magnitude & direction of the total force
on the wire?



Ans.
F
ab

= 0.60 N

z
-
direction;
F
bc

= 0.60 N

y
-
direction;
F
cd

= 0.849 N @ 45
0

above z=axis in
yz
-
plane;
F
de

= 0.60 N

y
-
direction;
F
net

=
F
de



[7] The r
ectangular 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 0.400
T, 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 the
z
-
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?



Ans. a) 0.0166 N m;

b) 0.0096 N m; c) 0.0166 N m; 0.0096 N m