Flux density:
Magnetic flux is the amount of magnetic field (or the number of lines of force) produced by a magnetic source. The symbol for magnetic flux is Φ (Greek letter ‘phi’). The unit of magnetic flux is the weber, Wb.
Magnetic flux density is the amount
of flux passing through a defined(specific) area that is perpendicular to the direction of the flux:
Magnetic flux density = magnetic flux / area
The symbol for magnetic flux density is B. The unit of magnetic flux density is the tesla, T, where 1 T = 1 Wb/m^2.
Hence,
B = Φ/A tesla , where A( m^2) is the area.
Numericals:
Problem 1.
A magnetic pole face has a rectangular section having dimensions 200 mm by 100 mm. If the total flux emerging from the pole is 150 µWb, calculate the flux density:
Solution.
Flux Φ = 150 µWb = 150 x 10^ -6 Wb
Cross sectional area A = 200 x 100 = 20000 mm^2
= 20000 x 10^ -6 m^2
Flux density B = Φ/A
= 150 x 10^- 6/20000 x 10^- 6
= 0.0075 T or 7.5 mT (Ans)
Problem 2.
The maximum working flux density of a lifting electromagnet is 1.8 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 353 mWb, determine the radius of the pole face:
Solution.
Flux density B = 1.8 T; flux Φ = 353 mWb = 353 x 10^-3 Wb
Since B = Φ/A
or
cross-sectional area, A = Φ/B
= 353 x 10^-3/1.8
= 0.1961 m^2
The pole face is circular, hence
area = π r^2, where r is the radius.
Hence π r^2 = 0.1961
from which r^2 = 0.1961/ π and radius r = (0.1961)^1/2 = 0.250 m
i.e. the radius of the pole face is 250 mm.
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