By Vladimir V. Mitin, Dmitry I. Sementsov
Modern know-how is swiftly constructing and hence destiny engineers have to gather complex wisdom in technology and know-how, together with electromagnetic phenomena. This ebook is a latest textual content of a one-semester direction for junior electric engineering scholars. It covers a vast spectrum of electromagnetic phenomena reminiscent of, floor waves, plasmas, photonic crystals, damaging refraction in addition to similar fabrics together with superconductors. moreover, the textual content brings jointly electromagnetism and optics because the majority of texts talk about electromagnetism disconnected from optics. by contrast, during this ebook either are mentioned. Seven labs were built to accompany the fabric of the ebook.
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Extra resources for An introduction to applied electromagnetics and optics
Solution. 12). Since the angle between E and the normal to the cylinder bases is 90°, the flux through both cylinder bases is zero. The total flux through the cylinder surface is ΦE=E2πrl, where r is the cylinder radius. The charge inside the cylinder is q = λ l. 42), ΦE=E2πrl=λlε0. Consequently, the magnitude of the electric field generated by an infinite uniformly charged line at a distance of r is E=λ2πrε0. 46) where φ is the electric potential and dφ = φ2−φ1. This expression relates the electric potential φ and the electric field vector: E⋅dl=Exdx+Eydy+Ezdz=−dφ.
20) Comparison of the left- and right-hand parts of this equation gives the following relation: ∇×B=μ0j. 3): ∇×B=| ijk∂∂x∂∂y∂∂zBxByBz |=i(∂Bz∂y−∂By∂z)+j(∂Bx∂z−∂Bz∂x)+k(∂By∂x −∂Bx∂y). Since the magnetic field lines are always closed, the flux of the vector B through any closed surface is zero. Thus, Gauss’s theorem for the vector B is given as ∮AB⋅dA=0. 24) This equation is one of the formulations of one of Maxwell’s equations known also as “Gauss’s law for the magnetic field,” and the earlier equation is consistent with Maxwell’s equation div B=0.
5 MAGNETIC FIELD IN A MEDIUM, MAGNETIC FIELD INTENSITY 1. Experiments show that the magnetic field produced by electric currents in a material differs from the magnetic field generated by the same currents in vacuum. A material placed in a magnetic field is magnetized and itself becomes a source of magnetic field. A magnetized material creates its own magnetic field B′ generated by microscopic currents. The absolute value of a ratio between B and B0 is called the relative magnetic permeability of the material κm = B/B0.