physics 202 chapter 32 oct 25, 2007icecube.wisc.edu/~karle/courses/phys202/202lecture16.pdf · 1...
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Physics 202Chapter 32Oct 25, 2007
Induction:Inductance,Self-Inductance,RL circuitEnergy of B-field
On whiteboard RL circuit
Solve Kirchhoff’s equation for the case of Switching on, in detail Switching off
Power Energy of B-field, dissipation in R
2
Demonstrations Eddy currents
Conducting plate entering localized strong B-field Discussion on whiteboard (remember the difference to a
plate moving inside a homogenous field!) Spherical magnet rolling slowly inside copper tube Magnet bouncing of a thick cold conducting copper plate
because of Eddy currents
RL circuit: voltage and current when switching onand off
Self-Inductance When the switch is
closed, the current doesnot immediately reach itsmaximum value
Faraday’s law can beused to describe theeffect: Close switch: I increases, dI/dt ≠0 ⇒ ΦΒ increases ⇒ Self-induced emf,
according to Faraday’s law ⇒ Induced current in
opposite direction ⇒ Net current is reduced.
!
" = #d$
B
dt%dI
dt
!
"L
= #LdI
dt
3
Self-Inductance, Coil Example
A current in the coil produces a magnetic field directedtoward the left (a)
If the current increases, the increasing flux creates aninduced emf of the polarity shown (b)
The polarity of the induced emf reverses if the currentdecreases (c)
Self-Inductance A induced emf is always
proportional to the timerate of change of thecurrent
L := inductance a measure of the
opposition to a change incurrent
L depends on thespecifics of the coil
Symbol for an inductor:
Inductance of a solenoidon the whiteboard
!
"L
= #LdI
dt
!
L = "#L
dI dt
A
sV1H1
!=
Unit: Henry (named for Joseph Henry)
4
RL Circuit, Analysis
An RL circuit contains aninductor and a resistor
When the switch is closed(at time t = 0), thecurrent begins to increase
At the same time, a backemf is induced in theinductor that opposes thechange, - the increasingcurrent.
RL Circuit, Analysis Applying Kirchhoff’s
loop rule to theprevious circuit gives
Looking at the currentand doing some math(whiteboard), we find
where τ = L / R
5
RL Circuit Applying Kirchhoff’s loop
rule:
This one is very easy tosolve. Separation ofvariables and integration(whiteboard) yields:
where τ = L / R
!
"IR " LdI
dt= 0
!
I ="
Re#Rt L
="
Re# t $
Energy in a Magnetic Field In a circuit with an inductor, the battery must
supply more energy than in a circuit without aninductor
Part of the energy supplied by the batteryappears as internal energy in the resistor
The remaining energy is stored in the magneticfield of the inductor
Compare to the energy stored in the electric fieldin a capacitor
!
U =1
2L " I
2
!
U =1
2C " #V( )
2
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