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Question 2: demonstration

Plan of the laboratory

Introduction

Question 1:

Question 2:

Question 3:

Applying Ampère's theorem on the same contour as before, a contour assumed to represent the medium direction of the magnetic flux in iron, we obtain:

(1)

The şi fields, in iron and, respectively, in the air-gap, are connected to the values of the corresponding inductions and through:

(2)

(3)

Considering the conservation of the flux, for we can write:

(4)

Combining ecuations (2) and (4), we can express field depending on induction:

(5)

Replacing this expression in (1) and considering (3), we obtain, in the end:

or:

(6)

The dependence of induction on the relay armature's position is represented in figure 5 for = 230 A.turns

Figure 5: The dependence of induction B according to position
 

We can observe that, unlike the case when the permeability of iron is considered infinite, the calculated value of the induction depends on the lenght of the magnetic circuit, the influence being greater when the polar faces of the two armatures are opposite . This result can be interpreted as a minimal reluctance of the magnetic circuit portion corresponding to the air-gap

(7)

The influence of the magnetic core's reluctance

(8)

upon the expression of the flux from the circuit

(9)

is, therefore, minimal.

The total flux connected to the reel is:

(10)

the being written as follows:

(11)

The electromagnetic torque, equal to the derivative in ratio to the magnetic co-energy's position (equal to the energy), expressed according to the current, is:

Considering (11), this can be written as

or :

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Last update: 2005, September, 30 | Translation: Sergiu Ivanov | Realization: Florin Ravigan, Cristian Vladu