1、Chapter 7 The Magnetic Field of Current,1 Basic Magnetic phenomenon,2 Magnetic Field and Magnetic Induction,3 The Law of BIOT And SAVART,4 Ampere circuital theorem,5 The magnetic field of moving charge,All electromagnetic phenomena are due to the charge and its moving.Charges generate electric field
2、s around them. If another charge were placed near them, that charge would experience a electric field force.Currents (the flow of charge) generate magnetic fields. A current in a magnetic field experiences a magnetic force. Electricity and magnetism are related. Where theres electricity, theres magn
3、etism. v.v.Example: dynamo、electromotor、transformer、telegraph、telephone、television、computer etc. All have to do with electromagnetism., 1 Basic magnetic phenomenon,2 Magnetic Field Magnetic Induction,1 Magnetic field 磁场,Magnetic field,Current or Magnet,Current or Magnet,2 Magnetic Induction 磁感应强度,Th
4、e magnetic force on motionless charges is zero.,The magnetic force on moving charges can be tested.,The electric field was defined by means of the force on the charge at rest,The magnetic field can be defined by examining the force on moving charges,Direction The force on moving charges is zero,Magn
5、itude,(T),3 Magnetic field lines 磁场（力）线,(1) The direction: The tangent direction of magnetic field lines at every point is the same as the direction of magnetic induction. 磁场线上任一点的切线方向和该点处的磁感应强度的方向一致。The magnitude: The crowding of iron filings(铁屑） near the poles of a magnet suggests that the strengt
6、h of the field is greater in those regions.磁场线密度表示该处磁感应强度的大小。Magnetic field lines outside a magnet flow from the north pole to the south pole, forming closed loops。The magnetic field lines have no source” or “sinks. 磁场线是闭合曲线，磁场是无源场,Several distributing of magnetic field line,A long straight wire,A c
7、ircular current,Magnetic field lines of a solenoid,4 Magnetic flux 磁通量,5 Gausss law for magnetism 磁场的高斯定理,The magnetic flux passing through a surface S is defined by the surface integral:,The total flux through a closed surface S is zero:,Appendix：Magnetic monopole 磁单极子,Magnetic charge: a single mag
8、netic monopole,Even today, physicists search for magnetic monopoles, but none has yet been found.,3 The Law of BIOT And SAVART,All carrying-current wire can be divided into many current elements.,A current element,gives,Direction：,Perpendicular to both the current element and the radial direction,Th
9、e total field,the magnetic field at point P,Magnitude：,the permeability of free space,Applications of BIOT- SAVART Law,Ex 1. Determine the B at a point P at distance r0 from wire. 0 , L, I,I,P,The right-hand rule shows that the field will be perpendicular to the plane containing the wire and the poi
10、nt P, and directed down into the page.,Question：on the extending line of wire:,Special example：Long wire:,Ex 2. Determine the magnetic field on the axis of a circular loop of wire at a distance r0 from the plane of the wire.,I,R,Choosing two current elements by central symmetry, the sum of B is dire
11、cted X axis .,The total B on the x axes:,Discuss：,(1) r0=0,(2) r0R,(3) N turns,r0=0,r0R,Magnetic moment 磁矩,Magnitude: Pm=I S,Direction:,Right-hand rule,N turns :,r0R,the direction of area vector,Ex 3. Determine the B of inside the solenoid. (L, I, n, 0),Inside the solenoid, the B every point are equ
12、ality.,Discuss：,Long straight solenoid：,Direction: axis direction,One end of half-solenoid:,4 Ampere circuital theorem, The law of closed path for electrostatic field,The Electrostatic field is conservative.,1 Ampere circuital theorem 安培环路定理, Is the same true for magnetic field? No.,The line integra
13、l of the magnetic induction around a closed path is equal to 0 times the algebraic sum of the currents,The rule of positive and negative of current I:,Notice：The currents depend on the direction of closed path.,2 Deriving Ampere circuital theorem,On the path 环路上,(2) For any closed curve that lies in
14、 a plane perpendicular to the wire and loops exactly once around the wire,(1) A circular path with the wire through its center,(3) A path with no wire,(4) Extending：The curve wraps around the wire N times,The sum of currents wraps L,The vector sum of Fields,Consider:,3 Application of Ampere circuita
15、l theorem,Amperes Law exhibits a basic relationship that holds between the magnetic field and electric current. It summarizes much of the experimental evidence found in the work of Biot and Savart, Ampere himself, and others.,Special demands:,(2) the magnetic field has the same direction at the path
16、,Amperes Law can sometimes be used to determine the magnetic field, especially when there is symmetry (对称性) and a path of integration can be found along which the magnetic field is constant in magnitude and has the same direction at the path. In that case, the line integral is simply the field stren
17、gth times the length of the path.,(1) the magnetic field is constant at the path,Ex 1 A toroid螺绕环 consists of a solenoid that is bend into a torus 环形线圈. If the toroid has N turns and carries current I, determine the B inside at a distance r from the axis of the the toroid.,r,From the symmetry, insid
18、e the toroid the magnetic field is constant at a fixed radius from the axis and that the magnetic lines are circular. 根据对称性，在与环共轴的圆周上，磁感应强度的大小相等，方向沿圆周的切线，即磁感应线是与环共轴的一系列同心圆。,Discuss:,The number of turns per unit length,Inside the toroid:,Conclusion:,Outside the toroid:,B=0,(螺绕环很细),当环的半径趋于无穷大，而维持单位长度上
19、的匝数 n 不变时，螺绕环就过渡到了无限长直的螺线管。,Average radius,(1) The magnetic field will be changed along with r Inside toroid .,(2),(1) Inside:,Ex 2 A solenoid consists of a wire coiled into a helix. Determine the B of the solenoid：0，n，I,When the turns are brought near to each other, the fields tend to cancel outsid
20、e the solenoid and to reinforce each other inside the solenoid.,a,b,c,d,Conclusion:,Direction: axes,(2) Half-infinite length,According to symmetry, the field is constant inside the solenoid and zero outside of it，the direction is parallel to axes.,Inside the wire: (rR),Ex 3 A long straight conductor
21、 carries current I uniformly distributed over its cross section. Find the B outside and inside the wire. R, I, 0,Outside the wire: (rR), P,r, P,r,dS,dS,L,The total current I is distributed uniformly over the total cross section of radius, the portion Ir through the smaller circle of radius r is :,r,
22、R,By symmetry the field lines are circular,5 The Magnetic Field of Moving Charge,Experiments indicate that the magnetic induction of a moving charge q is:,Magnitude:,Direction:,position vector,Angle between,Perpendicular to both the velocity and position vector,Ex 1 A long straight conductor carryin
23、g current I uniformly distributed over its cross section has a hole of radius a inside. The distance between two axis is b. Find the B at point P.,Using fill-in method to determine the field,L1：,L1,L2,All directions are shown in Fig,L2：,Ex 2 As shown in Fig, a wire(I) is coplanar with a closed wire
24、of rectangle，calculate the magnetic flux passing through the rectangle.,directed down into page,Ex 3 As shown in Fig, a current-carrying wire is coplanar with S1 and S2, the ratio of the flux passing S1 and S2 :,Notice：The magnetic flux through a closed surface is zero.,S1,S2,Ex 4 A thin sheet copper of width a carry current I which distributed uniformly across the sheet. Calculate the B at point P.,The field of a long straight wire:,Result:,directed down into page,
