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Magnetic Circuit Analysis Problems

This document contains 5 examples of calculating magnetic fields and fluxes in electrical machines. Example 1.1 calculates the current and permeability in a relay coil. Example 1.2 finds the flux density in a relay coil with a given current. Example 1.3 determines the air gap flux, density, and field intensity in a magnetic circuit. Example 1.4 calculates the flux, density, and inductance in a coil. Example 1.5 finds the flux density and inductance in a toroidal coil.

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Khalifa Mohamed
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180 views2 pages

Magnetic Circuit Analysis Problems

This document contains 5 examples of calculating magnetic fields and fluxes in electrical machines. Example 1.1 calculates the current and permeability in a relay coil. Example 1.2 finds the flux density in a relay coil with a given current. Example 1.3 determines the air gap flux, density, and field intensity in a magnetic circuit. Example 1.4 calculates the flux, density, and inductance in a coil. Example 1.5 finds the flux density and inductance in a toroidal coil.

Uploaded by

Khalifa Mohamed
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Higher Technological Institute/10th of Ramadan City

Department of Electrical & Computers Engineering

Electrical machines
Dr. Abdelhady Ragab
Sheet 1
Example 1.1
Figure 1.1 represents the magnetic circuit of a primitive relay. The
coil has 500 turns and the mean core path is lc= 360 mm. When
the air gap lengths are 1.5 mm each, a flux density of 0.8 tesla is
required to actuate the relay. The core is cast steel.
(a) Find the current in the coil.
(b) Compute the values of permeability and relative permeability of
the core.
(c) If the air gap is zero, find the current in the coil for the same
flux density (0.8 T) in the core.

Example 1.2
Consider the magnetic system of Example 1.1. If the coil current is
4 amps when each air gap length is 1 mm, find the flux density in the air gap.

Example 1.3
In the magnetic circuit of Fig, the relative permeability of the ferromagnetic material is 1200.
Neglect magnetic leakage and fringing. All dimensions are in centimeters, and the magnetic material
has a square cross-sectional area.
Determine the air gap flux, the air gap flux density, and the magnetic field intensity in the
air gap.
Example 1.4
For the magnetic circuit of Fig., N = 400 turns.
Mean core length lc= 50 cm.
Air gap length lg = 1.0 mm.
Cross-sectional area Ac = Ag = 15 cm2 .
Relative permeability of core μr = 3000.
i = 1.0 A.
Find
(a) Flux and flux density in the air gap.
(b) Inductance of the coil.

Example 1.5
The coil in Fig. has 250 turns and is wound on a silicon sheet steel. The inner
and outer radii are 20 and 25 cm, respectively, and the toroidal core has a
circular cross section. For a coil current of 2:5 A, find
(a) The magnetic flux density at the mean radius of the toroid.
(b) The inductance of the coil, assuming that the flux density within the core is
uniform and equal to that at the mean radius.

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