last class A--2010 物理双语课件

– the capacitor acts like short circuits
Qt 0 0, I t 0 Imax R
a b R I
ε
+q -q
C
After a long time, – the capacitor acts like open circuits.
I t 0, Q0 Qmax , Qt Qmax C

L
B dl 0
I
encl
• Magnetic fields produced by wires:
– solenoid of n turns per unit length:
• centre: • end:
B 0 nI B 0 nI 2
– inside a toroid of N closely spaced – of wire:
2 m qB

B dA

B dA 0
mv⊥ R qB
T
h Tv //
h
Review (4)
• The Hall effect:
EH vd B H EH l vd Bl
Magnetic force on current: b dF Idl B F I dl B
a b
R
I
Discharging a capacitor:
I 0 Imax Q0 RC
ε
+q
C
-q
RC Circuit
Charging a capacitor: Discharging a capacitor:
Q t Q0e t RC
Q t Q f 1 et
Qingdao University
Review (6)
Ampere’s law
– (1)the line integral of the B around any closed loop L
is – equal toμ0 times the total steady current I enclosed – by the loop.
Example4 :Find magnetic field produced by a disk with radius R，charge q, rotate around the axis. （利用积分）
Example5: find B in Coaxial Cable.
5.The solenoid has n turns of wire per unit length and carries a current I. Use Ampere’s law to find the field at or near the center of the solenoid.
dQ e t RC I t R dt
Discharging a CapaciБайду номын сангаасor
Q t Q0e t RC
dQ I et I 0 dt
RC
RC Circuit
• Charging a capacitor: • At t = 0 , the switch is closed to a
• Inductance:
total,another dI1 (2) M ? – mutual inductance: (1) 21 ? M I dt – self-inductance: (3) ? L dI (4) L ? total,self dt I
• Inductors in a circuit:
– right after the switch is closed, the inductor acts like – an open circuits. – after a long time, the inductor acts like a short circuit.
• Time constant of LR Circuits: • Energy in an inductor:
2.A long cylindrical conductor of radius R carries a current I as in the figure below. The current density J, however, is not uniform over the cross section of the conductor but is a function of the radius according to （I是否已知？ 如果是未知应该怎样计算）
E j
– macroscopic: V IR
• Resistance:
l R A
Review (2)
Kirchhoff’s laws
S Iin = S Iout
V 0
Charging a capacitor VC t 1 e t RC Q t C 1 e t RC
Ampere’s law
Forces on & Forces on btw currents currents
Review (1)
• Concepts:
E vd j nqvd I

j dA
• Electric current: I dq
dt
l
• Ohm’s law: – microscopic:
(6)
U ?
(5)
? L R
B2 u? 2 0
Energy density (7)
1 2 LI 2
• After a long time, the inductor acts like a short circuit. • If the switch is flipped away from the battery. • Using the modified Kirchhoff’s rule:
J br
where b is a constant. Find an expression for the magnetic field B (a) at a distance r1<R and (b) at a distance r2>R, measured from the axis.
Example3 :find Magnetic field of a circular current loops
dI L IR 0 dt I dI t R dI R dt dt I0 I 0 L I L I I0e t I R ln t I I0e Rt L I0 L 0.37I0 • L is a measure of an inductor’s • “resistance” to the change of current. • The larger L, the lower the rate of change of current.
NIA
Review (5)
ˆ • Biot-Savart law: dB 0 Idl r 4 r 2
0 b Idl r ˆ B 4 a r 2

• Fields produced by wires:
– distance r from long straight wire:
0

B dA 0

d B d E dl dt dt

B dA

d E B dl 0 I 0 0 dt
1. In the circuit below a number of resistors, currents, and battery emf’s are known. Others are not. Note in particular that we don’t even know which end of battery 2 is positive. •Use Kirchhoff’s rules to find the values of R3 and 2 •What is the potential difference between points a and b? •How much net power is being supplied to the circuit by • the two batteries?利用u· i即可
LR Circuits


Review(10)
• Displacement current:
• Maxwell’s equations:
dE Ic Id 0 dt
– in the absence of dielectric or magnetic materials,

Qin E dA
College Physics
Overview (part one)
Magnetic Field
Magnetic Field
Geometry description
Source of B B-S law
Character of B Guass’ law
Interaction with B Lorentz force Magnetic torque

a
- simplifies to F IL B if the magnetic field is uniform. Torque on a current loop in a magnetic B