EEE 498/598 Overview of Electrical Engineering. Lecture 7: Magnetostatics: Ampere’s Law Of Force; Magnetic Flux Density; Lorentz Force; Biot-savart Law; Applications Of Ampere’s Law In Integral Form; Vector Magnetic Potential; Magnetic Dipole; Magnetic Flux. Lecture 7 Objectives.
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Lecture 7: Magnetostatics: Ampere’s Law Of Force; Magnetic Flux Density; Lorentz Force; Biot-savart Law; Applications Of Ampere’s Law In Integral Form; Vector Magnetic Potential; Magnetic Dipole; Magnetic Flux
F12 = 0
unit vector in direction of current I1
unit vector in direction of current I2
unit vector in direction of force on I2 due to I1
unit vector in direction of I2 from I1
Permeability of free space
m0 = 4p 10-7 F/m
the magnetic flux density at the location of dl2 due to the current I1 in C1
Consider an infinite line current along the z-axis carrying current in the +z-direction:
(1) Assume from symmetry and the right-hand rule the form of the field
(2) Construct a family of Amperian paths
circles of radius r where
(3) Evaluate the total current passing through the surface bounded by the Amperian path
IMagnetic Flux Density of an Infinite Line Current Using Ampere’s Law (Cont’d)
(4) For each Amperian path, evaluate the integral
magnitude of B
(5) Solve for Bon each Amperian path
Because the above must hold for any
surface S, we must have
of Ampere’s Law
B is solenoidal
Magnitude of the dipole moment is the product of the current and the area of the loop.
Direction of the dipole moment is determined by the direction of current using the right-hand rule.