The document discusses magnetism and magnetic flux density. It provides examples of calculating relative permeability, magnetic flux density, induced voltage in a transformer, and the radius of a magnetic pole face using relationships between magnetic flux, flux density, area, turns ratio, and other variables. Formulas given include the definitions of magnetic flux density as magnetic flux divided by area and the relationship between magnetic flux, flux density, and radius for a circular pole face.

1. Magnetism

2. The graph above shows B-H curve for Cast Steel, what is the relative permeability (μr) of Cast Steel prior to
Saturation?
Note μ = ΔB/ΔH μ=μo x μr Assume the Permeability of free space (μo) is 12.57 x 10-7
The correct answer is: 597
(a) Slope of graph at 0.6Tμ =
0.6
800
= 0.75 𝑥10−3
Since μ=μo x μr at 0.6T
μr =
μ
μo
=
0.75 𝑥10−3
12.57 𝑥10−7 = 597
(b) Slope of graph at 1.6T = =
0.2
4000
= 0.05𝑥10−3
Since μ=μo x μr at 1.6T
μr =
μ
μo
=
0.05 𝑥10−3
12.57 𝑥10−7 = 39.8
Onset of
saturation

4. a

5. a

6. a

7. The force that will act on the wire is given by:
where F is force in N
B is the magnetic flux density in T
I is the current in Amps
l is the length of wire in the field in m
BIlF 

8. A conductor in a magnetic field experiences a force of 9.8N, when a current
of 6.1A is flowing. The length of wire in the uniform field is 183mm.
What is the magnetic flux density, B?
B =
𝐹
𝐼𝑥𝑙
• B =
9.8
6.1 𝑥183𝑥10−3 =
9.8
1.1163
= 8.779T
BIlF 

9. Transformer - theoretical
p
s
p
s
N
N
V
V

The transformer can be used to increase the voltage in a circuit
If the secondary has more turns than the primary, then the
output voltage will be higher than the input voltage
It is the ratio of the turns that determines the output ie
Power = Current x Volts
Watts (W) = Amps (I) x Volts (V)

10. Transformer
Transformer has 89 primary turns and 16 secondary turns.
• If the primary is supplied with an AC voltage of 71 V Peak to Peak,
what is the Peak to Peak Voltage induced at the Secondary?
71
=
16
89
= =
16𝑥71
89
= 12.76V
p
s
p
s
N
N
V
V

sV
sV

11. Flux Density
• If the pole face area of a magnet = 113.8mm x 117.7mm and the Flux (Φ) = 272μWb.
• Millimetres change to Metres
• Calculate the Flux Density in Tesla
Magnetic Flux Density = Magnetic Flux
Area
Magnetic Flux Density = 272𝑥10−6
= 0.0203T
0.1138 x 0.1177

12. Transformer
A transformer has 84 primary turns and 64 secondary turns.
• If the primary is supplied with a peak AC Voltage of 3.1 V and a peak AC
Current of 7.2 A, what is the maximum power at the Secondary?
(Assume no losses in the transformer)
Watts (W) = Amps (I) x Volts (V)
W = 7.2 x 3.1 = 22.32W

13. Magnetic Flux Density
• Magnetic flux, Φ, is the flux density divided by the area
• Magnetic flux density webers per metre2 B = Φ /Area
Magnetic Flux Density = Magnetic Flux
Area
where Magnetic Flux is in Wb and area is in m2
Magnetic Flux Density, B, depends on the current flowing

14. Radius of the pole face
The flux density (B) of a lifting electromagnet is 9.5 T and the area of its
pole face is circular in cross-section. If the total magnetic flux (Φ)
produced is 382 mWb, determine the radius of the pole face.
Magnetic Flux Density (B) = Magnetic Flux (Wb)
Area (π x 𝑟2
)
95 =
382𝑥10−3
π x 𝑟2
𝑟2 =
382𝑥10−3
9.5π
= 𝑟2 =
382𝑥10−3
29.85
= 𝑟 =√0.01278 = 𝑟 = 0.1131 m