EXERCISE 177, Page 401
1. What is the flux density in a magnetic field of cross-sectional area 20 cm 2
having a flux of
3 mWb?
Flux density, B =
 


A

20 10 m 2
= 1.5 T
2. Determine the total flux emerging from a magnetic pole face having dimensions 5 cm by 6 cm, if
the flux density is 0.9 T.
B


A from which, flux , B A 0.9 5 6 10

4
= 2.7 mWb
3. The maximum working flux density of a lifting electromagnet is 1.9 T and the effective area of a
pole face is circular in cross-section. If the total magnetic flux produced is 611 mWb determine
the radius of the pole face.
B


A


 r
2 from which, r
2 

B
 and radius, r =


  
B
 


1.9
 

3
= 0.32 m or 32 cm
4.
An electromagnet of square cross-section produces a flux density of 0.45 T. If the magnetic flux is
720

Wb find the dimensions of the electromagnet cross-section.
B


A from which, area, A


B


6
 
3
1.6 10 m
2
0.45
Let the side of the square section = x, then
2   
3 2 x 1.6 10 m and side, x =
 
3
1.6 10 m = 0.04 m = 4 cm
© John Bird Published by Taylor and Francis
407

i.e. the dimensions of the electromagnet cross-section = 4 cm by 4 cm
© John Bird Published by Taylor and Francis
408

EXERCISE 178, Page 404
1.
A conductor carries a current of 70 A at right-angles to a magnetic field having a a flux density
of 1.5 T. if the length of the conductor in the field is 200 mm calculate the force acting on the
conductor. What is the force when the conductor and field are at an angle of 45

?
Force, F = B I l sin

=

1.5 70 200 10 sin 90

= 21.0 N
When

= 45

, F = 21.0 sin 45

= 14.8 N
2.
Calculate the current required in a 240 mm length of conductor of a d.c. motor when the conductor
is situated at right-angles to the magnetic field of flux density 1.25 T, if a force of 1.20 N is to be
exerted on the conductor.
Force, F = B I l sin

i.e. 1.20 = 1.25 × I ×

3
240 10 × sin 90º from which, current, I =
1.20
  
3  sin 90

= 4.0 A
3.
A conductor 30 cm long is situated at right-angles to a magnetic field. Calculate the flux density
of the magnetic field if a current of 15 A in the conductor produces a force on it of 3.6 N
Force, F = B I l sin

from which, flux density, B =
F
I l sin



3.6
 
= 0.80 T
4.
A conductor 300 mm long carries a current of 13 A and is at right-angles to a magnetic field
between two circular pole faces, each of diameter 80 mm. If the total flux between the pole faces
is 0.75 mWb calculate the force exerted on the conductor.

When conductor and field are at right angles, force, F = B I l where B =
A
© John Bird Published by Taylor and Francis
409


Hence, force, F =
A

3
  
2 
6
   
3
= 0.582 N
5.
(a) A 400 mm length of conductor carrying a current of 25 A is situated at right-angles to a
magnetic field between two poles of an electric motor. The poles have a circular cross-section. If
the force exerted on the conductor is 80 N and the total flux between the pole faces is 1.27 mWb,
determine the diameter of a pole face.
(b) If the conductor in part (a) is vertical, the current flowing downwards and the direction of the
magnetic field is from left to right, what is the direction of the 80 N force?
(a) Force, F = B I l =

A

 r
2
from which, radius, r =
 
F
 

 
3  
80
 
 
3

7.1 10 m = 7.1 mm
Hence, diameter = 2

r = 2

7.1 = 14.2 mm
(b) By Fleming’s left hand rule, the direction of the force is towards the viewer .
© John Bird Published by Taylor and Francis
410

EXERCISE 179, Page 405
1.
Calculate the force exerted on a charge of 2 10

18 C travelling at
 6 m/s perpendicular to a
field of density
 
7
2 10 T .
Force, F = Q v B =
 
18   6   
7
=

19
8 10 N
2.
Determine the speed of a 10

19
C charge travelling perpendicular to a field of flux density 10

7
T,
if the force on the charge is 10

20
N.
Force, F = Q v B from which, speed, v =
F 10


19 
20

Q B 10 10

7
=
6
10 m/s
EXERCISE 180, Page 405
Answers found from within the text of the chapter, pages 395 to 405.
EXERCISE 181, Page 405
1.
(d) 2. (d) 3. (a) 4. (a) 5. (b) 6. (b) 7.
(d) 8.
(c) 9.
(d) 10.
(a) 11.
(c) 12.
(c)
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411