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Consider a toroidal solenoid wound on a non-magnetic core, such as shown in Fig. 20. If the flux density is measured on the centre line of the toroid, the relationship between B and H is given. b-y the straight line OA in Fig. 21. Ifnow the space within an unmagnetised ferromagnetic material, the well known magnetisation curve OBCDE, is obtained. The magnetisation has many names being referred to as :

B-H curve, the magnetic saturation curve, the virgin curve or simply the saturation curve. 

 

The difference in flux between the saturation curve and the air line, OA at any magnetising force,is due to the contribution of the magnetic material. This flux is known as the intrinsic flux and gives a true measure of magnetic properties than does the total flux, especially at very high m.m.fs, The point at which the intrinsic flux density curve becomes horizontal gives the intrinsic saturation.

The magnetisation curves can be determined by the following methods provided the materials are in the. form of a ring:

(i)   By means of a ballistic galvanometer

(ii)   By means of a fluxmeter.

The graphs in Fig. 22 show the relationship between the flux density (B) and the magnetic field obtained for different qualities ofiron. The data for mild steel, wrought iron and sheet steel are so similar that they can be represented by a common graph. Stalloy is an alloy of iron and silicon commonly used in the construction of transformers and A.C. machines.

Example 6. An air cored toroidal coil has 1500 turns and carries a current of 0.2 A The length of the magnetic circuit is 300 mm and cross-sectional area of the coil is 800 mm2. Calculate:

(i) Magnetic field strength,                                                                                        

(ii) Flux density, and

(iii) Total flux within the coil .

Solution. Number of turns, N = 1500

Current, I = 0.2 A

Length of the magnetic circuit, 1 = 300 mm = 0.3 m

Cross-sectional area of the coil, A = 800 mm2 = 800 × 10-6 m2

I.  Magnetic field strength, H : 

 

 

 

 

 

 

 

 

III.Total Flux within the coil, ɸ:

ɸ = B × A

= 1.256 × 10-3 × 800 × 10-6 = 1.005 × 10-6 Wb. (Ans.)

Example 7. A coil of 300 turns and of resistance 10 Ω is wound uniformly over a steel ring of mean circumference 30 cm and cross-sectional area 9 cm2. It is connected to a supply at 20 V.D.C. If rollll’ III’rlllc”ability of the ring is 1500, find: