Electrostatics Vs Magnetostatics Electrostatics Magnetostatics
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Electrostatics vs Magnetostatics Electrostatics Magnetostatics Stationary charges ⇒ Constant Electric Field Steady currents ⇒ Constant Magnetic Field Coulomb’s Law Biot-Savart’s Law 1 ̂ ̂ 4 4 (Inverse Square Law) (Inverse Square Law) Electric field is the negative gradient of the Magnetic field is the curl of magnetic vector electric scalar potential. potential. 1 ′ ′ ′ ′ 4 |′| 4 |′| Electric Scalar Potential Magnetic Vector Potential Three Poisson’s equations for solving Poisson’s equation for solving electric scalar magnetic vector potential potential. Discrete 2 Physical Dipole ′′′ Continuous Magnetic Dipole Moment Electric Dipole Moment 1 1 1 3 ∙̂̂ 3 ∙̂̂ 4 4 Electric field cause by an electric dipole Magnetic field cause by a magnetic dipole Torque on an electric dipole Torque on a magnetic dipole ∙ ∙ Electric force on an electric dipole Magnetic force on a magnetic dipole ∙ ∙ Electric Potential Energy Magnetic Potential Energy of an electric dipole of a magnetic dipole Electric Dipole Moment per unit volume Magnetic Dipole Moment per unit volume (Polarisation) (Magnetisation) ∙ Volume Bound Charge Density Volume Bound Current Density ∙ Surface Bound Charge Density Surface Bound Current Density Volume Charge Density Volume Current Density Net , Free , Bound Net , Free , Bound Volume Charge Volume Current Net , Free , Bound Net ,Free , Bound 1 = Electric field = Magnetic field = Electric Displacement = Auxiliary Field = Dielectric Polaristion = Magnetic Magnetization Polarisation is proportional to the electric field. Magnetization is proportional to the magnetic field. (Provided the electric field is not too strong) (Provided the magnetic field is not too strong) Note: Notice that the in is replaced by 1/ and not 1/ in in dielectric material 1/ in magnetic material in free space 1/ in free space 1 1 Permittivity of dielectric Permeability of material Permittivity of free space Permeability of free space Relative Permittivity Relative Permeability Electric Susceptibility Magnetic Susceptibility Note: Note: ϵ,ϵ0 , 0 Electric Susceptibility is a dimensionless Magnetic Susceptilibity is a dimensionless proportionality constant that indicates the proportionality constant that indicates the degree degree of polarization of a dielectric material in of magnetization of a magnetic material in response to an applied electric field. response to an applied magnetic field. 0 0 paramagnet M parallel 0 diamagnet M parallel 1 1 paramagnet M parallel 1 diamagnet M parallel Gauss’s law on net charges Amperes’s law on net current ‐ ‐ ‐ ‐ ∙ ∙ ∙ Differential Integral Differential Integral = Electric field = Magnetic field Gauss’s law on bound charges Ampere’s law on bound current ‐ ‐ ‐ ‐ ∙ ∙ ∙ Differential Integral Differential Integral = Dielectric Polaristion = Magnetic Magnetization Gauss’s law on free charges Amperes’s law on free current ‐ ‐ ‐ ∙ ∙ ∙ Differential Integral Differential Integral = Electric Displacement = Auxiliary Field Maxwell’s Equations Gauss’s law on Gaussian Surface Amperes’s law on Amperian Loop ∙ ∙ ∙ Differential Integral Differential Integral Electric field line diverges away from (towards to) a positive Magnetic field line curls around current. (negative) charge. Differential Integral Differential Integral 0 ∙ 0 ∙ 0 ∙ 0 Electrostatic field line does not curl, it diverges. Magnetic field line curls & loop. It does not diverges. No magnetic monopole. Lorentz Force .