Magnetic Circuits and Transformers Sattar Hussain firstname.lastname@example.org
1- Magnetic Field It is customary to represent the magnetic field by means of lines of forces that can be traced as a closed loops exiting at magnetic north pole and entering at magnetic south pole. These line are called flux lines . The flux lines take the least resistance path; that is, they are easier to set up in an iron medium than in the air.
The total number of flux lines is referred to as magnetic flux ϕ measured in weber (Wb) . The density of flux lines per unit of cross-sectional area perpendicular to the direction of the flux lines is called flux density, B , measured in Wb/m 2 or Tesla (T). The flux ϕ is then defined as the integral of the flux density over some surface area, A. If the flux is uniform over the cross sectional area A, then: ∫ = A BdA φ A B . =
The magnetic resistance that tends to oppose the establishment of magnetic flux lines is referred to as reluctance, ℛ . Reluctance of iron bar is much less than air reluctance. Hence, the iron bar is an easier path than air for flux lines. 2- Magnetic Field Produced by Currents A conductor carrying an electric current I exhibits a magnetic field in the space surrounding it.
The magnetic field is stronger near the conductor and decreases farther a way from it. The magnetic flux, ϕ , increases when the current , I increases. The direction of flux lines is determined by Ampere’s right-hand rule (RHR) . It states: when the thumb points to the current direction, the fingers point to the direction of magnetic field lines.
Since the cause of magnetic flux is the flow of electric current, for N-turn coil carrying a current I , the induced flux will be as a result of the product NI The quantity NI is called magnetomotive force (mmf) ℱ and its unit is ampere-turn (At) ℱ= magnetomotiveforce (mmf )= NI At Replacing the iron core with similar one having shorter mean (average) length , l , while maintaining the same mmf (At), would result in stronger magnetic field. This leads to another quantity called magnetic field intensity , or the magnetizing force H =magnetizing force=ℱ/ l = NI/l At/m
When the current or the number of turns is increased, the mmf ( ℱ) is increased, resulting in a higher flux ϕ ℱ α ϕ or ℱ = ℛϕ Ohm’s law for magnetic circuit similar to Ohm’s law in electric circuit ( V=RI ) thus: ℛ=reluctance=ℱ/ϕ The unit of ℛ is At/ Wb In analogous to the electric resistance , ℛ Where, μ is called the permeability of the material A l µ = A l A l R σ ρ = =
Permeability is a measure of a material’s property that relates to its ability to permits the establishment of the magnetic flux μ = μ r μ o Wb /( A.m )=H/m (H=Henry= Wb /A) Where μ r is the relative permeability μ o is the air permeability = 4 π x 10-7 H/m The relation between magnetic flux density, B, and magnetic field intensity, H, is: B=μ H
3- Electromagnetic Induction (Faraday’s Law)
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