《Electromagnetism, principles and application》教学课件（PPT讲稿）Chapter 8 Magnetic Fields：I

Chapter 8 Magnetic Fields: I Magnetic induction a The divergence of b Magnetic monopoles The Vector potentiala 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 See 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 uo is called the permeability of free space 10=4丌×10-7 tesla meter/ ampere Remark: the unit vector r1 points from the source to the point of observation i.e. from di to P. b has unit tesla

dB dI figure 8-l The magnetic induction dB=(Ho/4a)l dI x 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 dr and the magnetic induction expressed as r B 4丌 l-2 ere the integration is carried over the volume T'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 Φ=/sB·da Φ has unit weber

Example: Long Straight Wire Carrying a Current See Fig 8-3 dB dI Figure 8-3 The magnetic induction dB produced by an element i dl of the current I in a long straight wire

Example: Long Straight Wire Carrying a Current See Fig. 8-3