Lec05_Medium Properties.pdf

EE340 Electromagnetic Theory Fields in Matter 05-01-2024 EE340 EEE Institute of Technology Guwahati 1  Classification of Materials ❑ Based on Electrical Properties: ❖ Conductivity m...

EE340 Electromagnetic Theory Fields in Matter 05-01-2024 EE340 EEE Institute of Technology Guwahati 1  Classification of Materials ❑ Based on Electrical Properties: ❖ Conductivity measured in Siemens per meter S/m ❖ Depending on conductivity values, materials are classified as: ❖ Conductors ❖ Insulators or dielectrics ❖ Semiconductors ❖ Typically conductivity for conductors ~ 107 S/m ❖ For semiconductors: 100 - 10-4 S/m ❖ And for Insulators: < 10-4 S/m 05-01-2024 EE340 EEE Institute of Technology Guwahati 2  Currents 05-01-2024 EE340 EEE Institute of Technology Guwahati 3  Types of Current Conduction Current: Convection Current: ❑ It requires a conductor. ❑ It doesn’t require conductors. ❑ It Flows due to large number of free ❑ It Flows through medium in form of electrons in the conductor. electron beams. ❑ It does follows Ohm’s law ❑ It doesn’t follows Ohm’s law 𝑱 = 𝝈𝑬 05-01-2024 EE340 EEE Institute of Technology Guwahati 4  Convection Current 05-01-2024 EE340 EEE Institute of Technology Guwahati 5  Isolated Conductors A perfect conductor (𝝈 = ∞) cannot contain an electrostatic field within it. ❑ The free charges are available in conductor. ❑ They accumulate on the surface of the conductor and form an induced surface charge. ❑ The induced charges set up an internal induced field Ei, which cancels the externally applied field Ee. ❑ 𝑱 = 𝝈𝑬 ❑ 𝒊𝒇 𝝈 = ∞ 𝒕𝒉𝒆𝒏, 𝑬 = 𝟎 ❑ a conductor is equipotential medium since the electric potential is the same at every point. 05-01-2024 EE340 EEE Institute of Technology Guwahati 6  Conductors maintained at constant potential conductor whose ends are maintained at a potential difference V, ❑𝐸 ≠ 0 ❑ an electric field must exist inside the conductor to sustain the flow of current. It follows Ohm’s law: 05-01-2024 EE340 EEE Institute of Technology Guwahati 7  Polarization in Dielectrics 05-01-2024 EE340 EEE Institute of Technology Guwahati 8  Polarization in Dielectrics ❑ when molecules have permanent electric moments even in the absence of applied electric field. ❑ the average dipole moment is zero because of random thermal motion of molecules. ❑ Let’s assume t = 0, we switch off the existing external field, the polarization vector will exponentially decay due to thermalization: 𝑡 𝑃 𝑡 =𝑃 𝑒 𝑟 −𝑇 𝑇𝑟 𝑟𝑒𝑙𝑎𝑥𝑎𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 0 𝐷 𝑡 = 𝜖0 𝐸 𝑡 + 𝑃 𝑡 = 𝜖0 𝐸 𝑡 + 𝜖0 χ𝑒 𝑡 𝐸 𝑡 = 𝜖(t)𝐸 𝑡 τ −𝑇 𝜖 τ = 𝜖0 δ(τ) + 𝐴 𝑒 𝑟 𝐴 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑑𝑒𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝑢𝑝𝑜𝑛 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 05-01-2024 EE340 EEE Institute of Technology Guwahati 9  Polarization in Dielectrics 05-01-2024 EE340 EEE Institute of Technology Guwahati 10  Polarization in Dielectrics 05-01-2024 EE340 EEE Institute of Technology Guwahati 11  Magnetization in materials electrons orbit about a central positive nucleus; also spins around its own axis. Both these electronic motions produce internal magnetic fields 𝐵𝑖. The equivalent current loop has a magnetic Moment 𝑚 = 𝐼𝑏 𝑆 ෝ𝑎𝑛 The magnetization M, in amperes per meter, is the magnetic dipole moment per unit volume. Before B is applied After B is applied 05-01-2024 EE340 EEE Institute of Technology Guwahati 12  Magnetization in materials 05-01-2024 EE340 EEE Institute of Technology Guwahati 13  Classification 05-01-2024 EE340 EEE Institute of Technology Guwahati 14  Constitutive Relations A set of three relations, pertains to the properties of the medium, in which the electric field and magnetic field exists and propagate. 𝐷 = 𝜖𝐸 𝐷, E, B, H and J all are vector quantities. 𝐵 = 𝜇𝐻 𝜖, 𝜇 and σ are the material properties. 𝐽Ԧ = σ𝐸 Linear medium: when Constitutive parameters are not dependent upon applied field Homogenous medium: when Constitutive parameters are not dependent upon position. Dispersive medium: when Constitutive parameters are function of frequency. Isotropic medium: when Constitutive parameters are not dependent upon direction of the applied field. Otherwise they are called as anisotropic material. For anisotropic material constitutive parameters are in the form of tensor. 05-01-2024 EE340 EEE Institute of Technology Guwahati 15