Chapter 8 Magnetic Fields: I Magnetic Induction The divergence of B Magnetic Monopoles The vector potential a a and v Integral of a over a Closed curve
Chapter 8 Magnetic Fields:I ◼ Magnetic Induction ◼ The Divergence of B ◼ Magnetic Monopoles ◼ The Vector Potential A ◼ A and V ◼ Integral of A over a Closed Curve
8.1 The Magnetic Induction B ee FIg 8-1 a circuit carrying a current I generates the magnetic induction at the point Pas B X ri 4丌 where the integration is carried out over the circuit C and the constant po is called the permeability of free space. 10=4丌×10- tesla meter/ ampere Remark: the unit vector ri points from the source to the point of observation, i. e. from dl to P. b has unit tesla
dB dI Figure 8-l The magnetic induction dB=(Ho/4x)/dI x r/r produced by an element i dl of the current I in a circuit
If the current is distributed in space with a current den- sity J, then the element of current Idl is replaced by JdT, and the magnetic induction expressed as r B 4丌 Here the integration is carried over the volume occu pied by the currents Remarks: These two expressions for b are equivalent The flux of the magnetic induction b through a surface s is defined as =/sB·da Φ has unit weber
Example: Long Straight Wire Carrying a Current See Fig. 8-3 dR dI igure 8-3 The magnetic induction dB produced by an clement I dI of the current I in a long straight wire
Example: Long Straight Wire Carrying a Current See Fig. 8-3