大学物理稳恒磁场解读

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r the displacement from
I dl
I
Idl toward P.
dB
the contribution of Idl to the magnetic induction at point P.
r
P
B
the magnetic field of I at point P.
I
S
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I
Magnetic field lines surrounding a long and straight wires
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I
Magnetic field lines for a tightly wound solenoid of finite length carrying a steady current.

Gauss’ theorem
B dS 0

Ampere’s circulation theorem (Ampere’s Law) L B d l 0 Ii
i
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Affect of magnetic field force on currents
right hand rule
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Superposition Principle of Magnetic Induction
B d B
L
B Bi
u Idl r B d B＝ 4 r

L

0
L
3
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DISCUSSION
u Idl r B d B＝ 4 r
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Methods for Study

Contrast: electrostatic field.
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§13-1 Magnetic Induction B
How to quantify the magnetic field B ?
Electric field: investigate the result of the force exerted on a test point charge
I
Biot-Savart’s law
0 I d l r dB 4 r3
magnetic permeability of vacuum:
r
0 4 107 NA2
P Magnitude:
0 I d l sin dB 4 r2
Direction : Idl r
The strength of the field is proportional to the density of the lines.
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Magnetic field lines can never cross, meaning the field is unique at any point in space. The magnetic field lines are continuous closed loops without beginning or end. （therefore, the north and south poles cannot be separated . It is a distinct difference from electric field lines, which begin and end on positive and negative charges. If magnetic monopoles existed, then magnetic field lines would begin and end on them.）



Force on a moving charge f qv B L Force on a current-carrying wire dF Idl B Force on current-carrying loop M＝P B m
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Lorentz Force:
F qv B
The coefficient B is the function of position, it describes the natural quality of magnetic field at the position.
B dB
Biot-Savart law says that the magnetic field dB at point P created by an element of infinitesimal length dl of the wire.
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I dl
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For example, there is a moving point charge ,
Q 2 108 C
v 10m / s
F 1011 N
Magnetic force due to the earth’s field is usually negligible on any macroscopic object.
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Steady magnetic field :
Current element Idl
I
Direction: the direction of the current
I dl
Magnitude : I dl
r
P
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Difference Between the Current Element and the Point Charge: The point charge can exist independently. However, the current element can’t. (Because we must have a complete circuit for a current.)
I
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Properties of Magnetic Field Lines
The direction of magnetic field lines is defined to be the direction that the north end of a compass needles points, i.e., it is tangent to the field line at any point in space.
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The electric force does work in displacing a charged particle, whereas the magnetic force associated with a steady magnetic field does no work when a charged particle is displaced.
E＝F / q
Magnetic field: investigate the result of force exerted on a moving test point charge (Lorentz force) Demand?
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Results
q 18/9/27 18
Magnetic Induction B
Fm Magnitude : B qv sin
Fm
Direction :
B
v
Unit : tesla (T) (brilliant inventor Nikola Tesla,1856-1943 )
F qvB sin
F B qv sin
F
F
q

B

v
B
v

The right –hand rule
＝0， F 0
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DISCUSSION
F qv B
The electric force is always parallel or antiparallel to the direction of the electric field, whereas the magnetic force is perpendicular to the magnetic field. The magnetic force acts on a charged particle only when the particle is in motion.
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Superposition of Magnetic Induction
B Bi
i
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§13-2 Biot-Savart Law
STRATEGY Electrostatic field :
Q dQ dE E dE
I Id l dB B dB

r

L

0
L
3
is a vector directed from the current element toward
the field point. The integral is a vector operation and must reduce it to a
1N 1N 1T C m / s Am
Another smaller unit: gauss (G),
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1 G 104 T
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Magnetic Force Due to the Earth’s Field is usually small.
The earth’s magnetic field on its surface is only about 0.5G. B 5 105 T
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MAIN CONTENTS

Magnetic field produced by currents. F max Representation ： B＝ Fmax v B qv Rules ：

u0 Idl r Biot-savart’s law B 4 r 3
q


B
v
The force acted on the moving point charge by magnetic field is called Lorentz force. the Lorentz force acted on the charge is related with its electric quantity , instantaneous position, and its velocity.
Steady Magnetic Field : invariable with time/ produced by steady current. unstable magnetic field.
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Perceptual Knowledge
例2
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Pictorial Representation of Magnetic field N Magnetic field lines surrounding a current loop. The field pattern is axially symmetric.
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Steady Magnetic Field in Vacuum
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Steady Magnetic Field in Vacuum
Vacuum: without medium.
Magnetic Field : a vector field which exerts a magnetic force on moving electric charges