1. Magnetic induction intensity
Magnetic induction intensity is a physical quantity used to describe the properties of the magnetic field, expressed by B, the direction of B at a point in the magnetic field is the direction of the magnetic field at the point, and the size of B indicates the strength of the magnetic field at the point.
In the SI system of units (International System of Units), the unit of magnetic induction strength is [volts · second/meter 2], and [volts]·[second] is called Weber, so the unit of magnetic induction strength is called [Weber/meter 2] or [Tesla], referred to as [T], in the CGSM system of units, the unit of magnetic induction strength is [Gauss]. The units are denoted by symbols: V is [volts], s is [seconds], m is [meters], Wb is [Weber], T is [T], Gs is [Gauss], mT is [millite].
1T = 1Wb/m2=104Gs=103mT (1)
2, magnetic line of force, magnetic flux and magnetic flux continuity theorem
Magnetic field is depicted graphically with magnetic field lines. The magnetic field lines of various magnetic fields generated by current are shown in Figure 1. Magnetic field lines are headless and tailless closed lines surrounding the current, and the direction of current and the direction of return of magnetic field line conform to the right-hand rule.
We specify that the tangent direction of any point of the magnetic field line is the direction of the magnetic field (i.e., B) at that point, and that the number of magnetic field lines per unit area perpendicular to the B vector is equal to the magnitude of the B vector at that point. In other words, where the magnetic field is strong, the magnetic field line is denser, and where the magnetic field is weak, the magnetic field line is thinner.
The total number of lines of magnetic force passing through a surface is called the magnetic flux passing through the surface and is represented by Φ. The calculation of magnetic flux is shown in Figure 2. The area element is taken on the surface, and a θ Angle is formed between the direction of its normal line and the direction of B of the point. The magnetic flux of the element passing through the area is:
dφ=B×cosθ×ds (2)
So the total flux of S through the surface is
φ = # B×cosθ×ds (3)
When B is uniform and S is a plane and perpendicular to B, the magnetic flux through the S plane is:
φ = B×S (4)
This is a relationship that is often used in magnetic measurements.
Continuous flux theorem: When the S-plane is a closed surface, because the magnetic field line is a closed line, then the magnetic field line through the closed surface must be through the other parts of the closed surface, so the total magnetic flux through any closed surface must be equal to zero. To wit:
φ = # Bcosθds = 0 (5)
The unit of the magnetic flux is [Weber] in the SI system of units, [Maxwell] in the CGSM system of units, and the abbreviation [Mai] symbol is represented by Mx.
1Wb=108Mx (6)
3, magnetic field strength, permeability and ampere-loop law
Magnetic field strength is a physical quantity introduced to facilitate the analysis of the relationship between magnetic field and current, it is also a vector, expressed by H, its relationship with magnetic induction intensity is:
H = B/μ (7)
Where: μ is the permeability of the magnetic medium, determined by the nature of the magnetic medium
Agreed. In SI units, the permeability of a vacuum is:
μ0 = 4π×10-7 Henry/m (8)
The unit of H is [ampere/meter], in the CGSM system of units, the permeability of a vacuum is 1, and the unit of H is [Oster], short for [Ao]. The units are represented by symbols: A is [ampere], Oe is [O], and H is [Henry].
1A/m = 4π×10-3 Oe (9)
Ampere's loop law: In a magnetic field, the H vector follows an arbitrarily closed curve
The line integral of sigma is equal to the algebraic sum of the currents enclosed in this closed curve. To wit:
# H×cosα×dl=∑I (10)
Where: α is the Angle between the tangent direction of the curve and the magnetic field direction of the point.
By using the Ampere-loop law, we can easily calculate the magnetic field generated by a current with a certain spatial symmetry. For example, calculate the magnetic field strength at the P point inside a uniformly tightly wound circular solenoid, as shown in Figure 4. Take the concentric circles of radius r through point P as the closed integral curve. Due to the symmetry relationship, the magnetic field strength at each point around the concentric circle is equal, and the direction of the magnetic field strength is along the tangent direction of the concentric circle, that is, α = 0, so:
# H×cosα×dl = H*2πr = NI (11)
So the magnetic field strength at point P: H = NI/ (2πr)
Where N is the number of winding turns. From this relationship, it can be seen that the strength of the magnetic field is determined only by the distribution of the current that generates the magnetic field, and has nothing to do with the properties of the magnetic medium.