Area of hysteresis loop is equal to work required to re-magnetize the ferromagnet.

Variations in Hysteresis Curves

 

Coercivity and Remanence in Permanent Magnets

A good permanent magnet should produce a high magnetic field with a low mass, and should be stable against the influences which would demagnetize it. The desirable properties of such magnets are typically stated in terms of the remanence and coercivity of the magnet materials.

 

Description of laboratory research facility and methodology of measurements

Magnetic properties of ferromagnetics are investigated in this work. In order to do this the circular core, made from investigated material, is winded by two coils: primary, with the number of winds N 1 and secondary, with N 2, which are switched in a circuit as it’s shown in a protocol below, where: T – torus; N 1 – primary coil; N 2 – secondary coil; P – potentiometer; mA – miliamperemeter; C – capacitor; R 1 and R 2 – resistors with known resistance; ЭO – cathode-ray oscilloscope.

In order to obtain a hysteresis loop on oscilloscope screen the voltage proportional to the magnitude of induction B should be applied to vertical plates (y - terminals) of cathode-ray tube and voltage proportional to the magnitude of intensity H - to horizontal plates (x - terminals).

Let us prove that the voltage on a resistor R 1 in a primary coil circuit is proportional to H and voltage on a capacitor C is proportional to B.

There is alternating current i from external source in a primary coil circuit. Magnetic field intensity in a torus is:

H = i 1 n 1,

where n 1 – is number of coils of primary coil per unit length of a torus.

The voltage on a resistance R 1 is:

U 1 = i 1 R 1.

Considering i 1 = Н / п 1, obtain

(1)

This voltage is applied to horizontal plates of oscilloscope.

The alternating current in a primary coil causes appearance of induced EMF in a secondary coil, which is proportional to rate of change of magnetic flux:

.

The magnetic flux, piercing cross-sectional area of a torus is:

Ф = ВS.

Hence,

.

This EMF will cause the appearance of a current in secondary coil circuit:

.

The resistance of secondary coil circuit might be taken R 2, as long the resistance of capacitor is rather small, with respect to R 2. The voltage on a capacitor:

.

Now we put the value of i 2 in equation for Uc and evaluate it:

.

This voltage is proportional to magnetic field induction B. It is applied to vertical plates of oscilloscope.

(2)

Thus, the deviation of cathode ray trace on a screen of oscilloscope is proportional to H on horizontal, and to B on vertical. It will trace B = f(H) – curve 50 times per second because the frequency of a current is 50 Hz. The limits in which H changes, can be changed by changing the amplitude of i 1in a primary coil.

The main hysteresis loop will appear when the limits of change of H is such that the ferromagnetic magnetize till saturation; the secondary loops will appear in opposite case. Peaks of all secondary loops lies on main magnetization curve. Hence, in order to obtain main magnetization curve the coordinates nx and ny of secondary loops peaks has to be measured.

By knowing the voltages ux and uy, which rejects the ray on one scale grid, the magnitudes of voltages Ux and Uy can be defined:

Ux = nxиx,

Uy = nyиy.

Magnitude of H can be defined from (1) as:

.

п 1, R 1, r stay permanent during this work, its magnitudes is on apparatus, so the last equation can be evaluated as:

H = kxnx

(3)

where .

Equation for induction B we’ll obtain from (2):

,

or .

(4)

where

(5)

kx and ky has to be calculated on known initial data before measurements.

Experimental task for this work is to plot magnetization curve (B vs H) and µ vs H curve.

In order to do this we use oscilloscope with image of hysteresis loop on its screen and potentiometer. By decreasing current with the help of potentiometer form maxim value to minimum we measure coordinates nx and ny of vertices of obtained hysteresis loops. Then, by equations (3) and (4) calculate B and H. Calculating permeability as we plot B and µvs H dependencies on one graphic.

Description of laboratory research facility and methodology of measurements

Data processing

(Same as in Laboratory work № 2-2).