Magnetic circuit concept
Keypoints:
1. Define Magnetic Field.
2. Properties of magnetic lines of force.
3. Magnetic circuit.
4. Important terms and definitions.
1. Magnetic field.
2. Magnetic flux.
3. Magnetic flux density.
4. Permeability.
5. Relative permeability.
6. Magnetic field intensity.
7. Magnetomotive force.
8. Reluctance.
9. Permeance.
10. Reluctivity.
• Define Magnetic Field
A region around a magnet where its poles exhibit a force of attraction or repulsion is called magnetic field.
• Properties of magnetic lines of force
1. The magnetic flux lines originate from N-pole and terminates at S-poles outside the magnet but from S-pole to N-pole from inside the magnet.
2. They form a closed loop.
3. They always follow the least reluctance path.
4. They never intersect each other.
5. They repel each other when they are parallel and are in the same direction.
6. They remain unaffected by non-magnetic materials.
• Magnetic circuit
Definition:- The closed path followed by magnetic flux is called a Magnetic Circuit. A magnetic circuit consists of a high permeability materials like iron, soft Steel, etc. The magnetic flux start from a point and finishes at the same point after completing its path. Figure 1.1 shows a solenoid having N turns wound on an iron core (ring). When current I ampere passesd through the solenoid magnetic flux ø Wb (1Weber = 10⁸ Maxwell) is set-up in the core.
Fig:- 1.1 Magnetic Circuit
Let, l = mean length of magnetic circuit in. meter;
a = area of cross-section of core in m²;
μᵣ = relative permeability of core material;
Flux density in the core material,
B = ø/a ............Wb/m²
Magnetising force in the core material,
H = B/μ₀ μᵣ = (ø/a μₒ μᵣ) ........AT/m
As per work law, the work done in moving a unit pole once round the magnetic circuit or path is equal to the ampere- turns enclosed by the magnetic circuit.
i.e.,. Hl = NI or (ø/a μₒ μᵣ) × l = NI
or ø = NI / (l/a μₒ μᵣ) Wb ..............(i)
Where, S = l/a μₒ μᵣ
S = Reluctance
Therefore, Flux = mmf / Reluctance
Expression (i), reveals that the amount of flux set-up in the core is:
1. directly proportional to N and I i.e., NI called magnetomotive force (mmf).
2. inversely proportional to l/a μₒ μᵣ called reluctance of the magnetic path. The lower is the reluctance, the higher will be the flux and vice-versa.
We know that, Flux = mmf / Reluctance
Above expression is analogous to Ohm's law for electric current, I = emf / resistance. The mmf is analogous to emf in electric circuit, reluctance is analogous to resistance and flux is analogous to current. Hence, above expression is sometimes referred to as Ohm's law of magnetic circuits.
Important Terms and Definition:
1. Magnetic field:- A region around a magnet where its pole exhibit a force of attraction or repulsion is called magnetic field.
2. Magnetic flux:- When current passed through a magnetic circuit magnetic lines of force are set-up, this is known as magnetic flux. Its unit is Weber (Wb) and it is analogous to electric current I in electric circuit.
3. Magnetic flux density:- The magnetic flux density at a point is the flus per unit area at right angle to the flux at that point. It is represented by letter B and its unit is Wb/m² or Tesla.
B = ø/a ............Wb/m²
1Weber = 10⁸ Maxwell.
4. Permeability:- The ability of a magnetic material to conduct magnetic lines of force through it is called permeability of that material. It is represented by μ (a Greek letter mu), the greater the permeability of the material, the greater is its conductivity for the magnetic lines of force and vice-versa. Permeability for air or vacuum is the poorest and denoted by μₒ.
where, μₒ = 4Ï€ × 10⁻⁷ H/m
5. Relative permeability:- Generally, the absolute or actual permeability μ of a magnetic material is very higher as compared to absolute permeability (μₒ) of a vacuum or air. So, relative permeability is calculated in comparison with air or vacuum.
Hence, the ratio of permeability μ of a magnetic material to the absolute permeability μₒ of a vacuum or air is called the relative μᵣ of the material.
i.e., μᵣ = μ / μₒ or μ = μₒ μᵣ ..........(ii)
Thus, from equation (ii) it is evident that the relative permeability of a vacuum or air would be μₒ / μₒ = 1. Moreover, the value of relative permeability for all non magnetic material is also 1.
μᵣ = 8000 for soft iron.
For mumetal (iron 22 %, Nickel 78 %) is as high as 1,20,000.
6. Magnetic field intensity:- The force acting on a unit north pole of 1Wb placed in the vicinity of the magnetic field is called magnetising force or magnetic field intensity. It is represented as H and measured in AT/m.
H = m.m.f / length of magnetic path
H = NI / l ...........AT/m
Magnetic field intensity is a vector quantity, possessing both magnitude and direction. In vector form, it is given by;
Ĥ = (m / 4πμₒμᵣd² )d̂
Where, m = pole strength in Wb.
d = distance of a point at which magnetic field strength has to be calculated from a pole of strength m Wb.
If a pole of m Wb is placed in a uniform magnetic field of strength H newton/Wb, then force acting on a pole, F = m H newtons.
7. Magnetomotive force (mmf):- A magnetic pressure that set-up or tends to set-up magnetic flux in a magnetic circuit is called magnetomotive force. According to work law it is defined as:
The work done in moving a unit magnetic pole once around the magnetic circuit is called the magnetomotive force (m.m.f.).
m.m.f. = NI ampere-turns (AT)
Magnetomotive force is analogous to e.m.f. in an electric circuit.
8. Reluctance:- The opposition offered by the magnetic circuit to the magnetic flux is called reluctance. It depends upon length of the magnetic path (l), area of x - section (a) and permeability (μ = μₒ μᵣ)of the magnetic material that makes up the magnetic circuit. It is measured in AT/Wb. It is analogous to resistance in an electric circuit.
Reluctance, S = l / (a μₒ μᵣ) AT/Wb
9. Permeance:- It is reciprocal of reluctance and is a measure of the ease with which flux can set-up in the magnetic circuit.
Permeance = 1 / Reluctance
Permeance = (a μₒ μᵣ) / l ......Wb/AT or H
It is analogous to conductance in an electric circuit.
10. Reluctivity:- It is specific reluctance and corresponds to resistivity in an electric circuit.