EEE340Lecture 231 6-5: Magnetic Dipole A circular current loop of radius b, carrying current I makes a magnetic dipole. For R>>b, the magnetic vector potential.

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EEE340Lecture 231 6-5: Magnetic Dipole A circular current loop of radius b, carrying current I makes a magnetic dipole. For R>>b, the magnetic vector potential at a point P(r, ,  /2) is where is the magnetic moment, Using we have the B-field (6.45) (6.48)

EEE340Lecture 232 Equations (6.45) and (6.48) the dual of the electric dipole. where is the electric dipole moment. (3.53b) (3.54)

EEE340Lecture 233 6-6 Magnetization and Equivalent current Density The magnetization vector In contrast to the polarization vector The equivalent volume current density and surface current density These two equations are the dual of (A/m) (6.55) (C/m 2 ) (3.79) (6.62) (6.63) (3.89) (3.88)

EEE340Lecture 234 6-7: Magnetic field Intensity and Relative Permeability The magnetic field (intensity) H is defined as Or where  m is magnetic susceptibility In contrast (A/m) (6.75) (Wb/m 2 ) (6.80) (6.79) (3.102) (3.97)

EEE340Lecture 235 Substance Susceptibility  m Vacuum 0.00 Ferromagnetic, Fe, Co, Ni, Mn, Mg 6-9 Behavior of Magnetic Materials

EEE340Lecture 236 We know that For region  < a, the inner conductor the uniform current density is x Example. Infinitely Long Coaxial Transmission Line with uniform J

EEE340Lecture 237 Therefore, Applying Ampere’s law, we get For region b <  < c

EEE340Lecture 238 For the outer conductor the uniform current density is Ampere’s law gives

EEE340Lecture 239 Example. Find of a straight wire carrying current I, and making angles Solution Employing (6.33c) where dz’ R P(x,y,0) (0,0,z’) 0 A B

EEE340Lecture 2310 To integrate, we employ variable transformation Hence Finally, It reduces to (6-35) when (6-35) general

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