What is the source of magnetism in matter? A rod made of a ferromagnetic materia

Question

What is the source of magnetism in matter? A rod made of a ferromagnetic material characterized by the hysteresis loop shown in the figure below. If the rod is 50 cm long, with a circular cross-section, 1 cm2 in area:

(i) Calculate the pole strength of the rod after being magnetized to saturation and removed from the magnetizing field.

(ii) Calculate the magnetic field intensity of the rod at a point in line with the rod 50 cm from its nearest end.

(iii) Compute the magnetic field (H) required to align the dipole m (Figure 3) at room temperature (300 oK) given that:

m = 1.85 x 10-23 A m2,
Aligning energy: Em = m*H; and -16 Thermal energy: ET = k T; k = Boltzmann constant = 1.38 x 10 erg/ K

Explanation / Answer

What is the source of magnetism in matter?

Ans - Magnetism is a force generated in matter by the motion of electrons within its atoms. Magnetism and electricity represent different aspects of the force of electromagnetism, which is one part of Nature's fundamental electroweak force. The region in space that is penetrated by the imaginary lines of magnetic force describes a magnetic field. The strength of the magnetic field is determined by the number of lines of force per unit area of space. Magnetic fields are created on a large scale either by the passage of an electric current through magnetic metals or by magnetized materials called magnets. The elemental metals-iron, cobalt, nickel, and their solid solutions or alloys with related metallic elements-are typical materials that respond strongly to magnetic fields. Unlike the all-pervasive fundamental force field of gravity, the magnetic force field within a magnetized body, such as a bar magnet, is polarized-that is, the field is strongest and of opposite signs at the two extremities or poles of the magnet. Magnetism arises from two types of motions of electrons in atoms-one is the motion of the electrons in an orbit around the nucleus, similar to the motion of the planets in our solar system around the sun, and the other is the spin of the electrons around its axis, analogous to the rotation of the Earth about its own axis. The orbital and the spin motion independently impart a magnetic moment on each electron causing each of them to behave as a tiny magnet. The magnetic moment of a magnet is defined by the rotational force experienced by it in a magnetic field of unit strength acting perpendicular to its magnetic axis. In a large fraction of the elements, the magnetic moment of the electrons cancel out because of the Pauli Exclusion Principle, which states that each electronic orbit can be occupied by only two electrons of opposite spin. However, a number of so-called transition metal atoms, such as iron, cobalt, and nickel, have magnetic moments that are not cancelled; these elements are, therefore, common examples of magnetic materials. In these transition metal elements the magnetic moment arises only from the spin of the electrons.

(i) Calculate the pole strength of the rod after being magnetized to saturation and removed from the magnetizing field.

Ans - Electromagnets are basically coils of wire which behave like bar magnets with a distinct north and South Pole when an electrical current passes through the coil. The static magnetic field produced by each individual coil loop is summed with its neighbor with the combined magnetic field concentrated like the single wire loop of the coil. The resultant static magnetic field with a north pole at one end and a south pole at the other is uniform and a lot stronger in the center of the coil than around the exterior. The formula therefore for calculating the “Magnetic Field Strength”, H sometimes called “Magnetizing Force” of a long straight current carrying conductor is derived from the current flowing through it and the distance from it.

Where:

H – is the strength of the magnetic field in ampere-turns/meter, At/m

N – is the number of turns of the coil

I – is the current flowing through the coil in amps, A

L – is the length of the coil in meters, m

The magnetic field strength of the electromagnet also depends upon the type of core material being used as the main purpose of the core is to concentrate the magnetic flux in a well-defined and predictable path. So far only air cored (hollow) coils have been considered but the introduction of other materials into the core (the center of the coil) has a very large controlling effect on the strength of the magnetic field. The magnetic pole strength (units of Webbers) of a permanent/bar magnet is calculated by moving the bar magnet past an "infinite" wire and measuring the current it creates. The formula is:

P = W / I,

Where:

p = Magnetic Pole Strength (Wb) (p>0 for North)

W = Work done moving pole around infinite wire (J)

I = Current in infinite wire (A)

Therefore P = 10 ampere meter.

(ii) Calculate the magnetic field intensity of the rod at a point in line with the rod 50 cm from its nearest end.

Ans -

To measure magnetic field intensity, usually Place the sensor on a magnet face to measure the field. With a resolution of 1 Gauss, it can measure small variations from magnet to magnet or it can detect if a given magnet has lost strength and note the readings. Magnetic field strength is one of two ways that the intensity of a magnetic field can be expressed. Technically, a distinction is made between magnetic field strength H, measured in amperes per meter (A/m), and magnetic flux density B, measured in Newton-meters per ampere (Nm/A), also called teslas (T). The magnetic fields generated by currents and calculated from Ampere's Law or the Biot-Savart Law are characterized by the magnetic field B measured in Tesla. But when the generated fields pass through magnetic materials which themselves contribute internal magnetic fields, ambiguities can arise about what part of the field comes from the external currents and what comes from the material itself. It has been common practice to define another magnetic field quantity, usually called the "magnetic field strength" designated by H. It can be defined by the relationship:

H = B0/meu0 = B/meu0 – M = 2*10-5 T.

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