Energy can be stored in electric fields
Eone _ plate =Q / A( )2!0
(for small s)
sAAQUel !""#
$%%&
'=!
2
00
/21
((
E volume
!Uel
! volume( ) =12"0E
2Field energy density: (J/m3)
Energy expended by us was converted into energy stored in the electric field
Energy Density of Electric Field
Fby _ you = QE = Q(Q / A)2!0
!Uelectric = Fby _ you!s = Q(Q / A)2"0
!s
Energy Density of Electric Field
In the previous slide, the “system” is the set of two plates. Work, Wexternal > 0, is done on the system by you – part of the “surroundings.”
!Esystem = !KE + !Uelectric =Wexternal
If the force exerted by you just offsets the attractive force, Fby-plates, so that the plate moves with no gain in KE,
!Uelectric =Wexternal = Fby _ you!s
In a multiparticle system we can either consider a change in potential energy or a change in field energy (but not both); the quantities are equal.
The idea of energy stored in fields is a general one: Magnetic and gravitational fields can also carry energy.
The concept of energy stored in the field is very useful:
- electromagnetic waves
Potential Energy and Field Energy
e+ e-
System Surroundings
Release electron and positron – the electron (system) will gain kinetic energy
Conservation of energy → surrounding energy must decrease
Does the energy of the positron decrease? - No, it increases
Where is the decrease of the energy in the surroundings? - Energy stored in the fields must decrease
An Electron and a Positron
e+ e-
System Surroundings
Single charge:
21~r
E
Dipole:
31~r
E (far)
Energy:
dVE! 202
1 "
Energy stored in the E fields decreases as e+ and e- get closer!
An Electron and a Positron
e+ e-
System Surroundings
Δ(Field energy) + ΔKpositron + ΔKelectron = 0
Δ(Field energy) = -2(ΔKelectron )
Principle of conservation of energy:
Alternative way: e+ and e- are both in the system:
ΔUel = -2(ΔKelectron )
Change in potential energy for the two-particle system is the same as the change in the field energy
An Electron and a Positron
Chapter 18
Magnetic Field
In 1935, fictional industrialist Diet Smith, a friend of cartoon detective Dick Tracy, predicted that “the nation that controls magnetism will control the universe.”
A compass needle turns and points in a particular direction
there is something which interacts with it
Magnetic field (B): whatever it is that is detected by a compass
Compass: similar to electric dipole
Magnetic Field
Magnetic fields are produced by moving charges Current in a wire: convenient source of magnetic field Static equilibrium: net motion of electrons is zero Can make electric circuit with continuous motion of electrons
The electron current (i) is the number of electrons per second that enter a section of a conductor.
Counting electrons: complicated
Indirect methods: measure magnetic field measure heating effect
Electron Current
Both are proportional to the electron current
If 1.8×1016 electrons enter a light bulb in 3 ms – what is the magnitude of electron current at that point in the circuit?
selectrons/ s
electrons 183
16
106103
108.1 !=!
!== "tNi
Exercise
Tungsten filament
Use socket
Thinner filament wire
Simple Circuits
Inert gas
We will use a magnetic compass as a detector of B.
How can we be sure that it does not simply respond to electric fields?
Interacts with iron, steel – even if they are neutral
Unaffected by aluminum, plastic etc., though charged tapes interact with these materials
Points toward North pole – electric dipole does not do that
Detecting Magnetic Fields
Compass needle:
Make electric circuit:
What is the effect on the compass needle? What if we switch polarity? What if we run wire under compass? What if there is no current in the wire?
Use short bulb
The Magnetic Effects of Currents
Make electric circuit:
Needle deflection at different currents: change light bulb (to long one) short-circuit: two batteries, no light bulb
The Magnetic Effects of Currents
Current-Carrying Wire & Compass
Conclusions: • The magnitude of B depends on the amount of current • A wire with no current produces no B • B is perpendicular to the direction of current • B under the wire is opposite to B over the wire
Oersted effect: discovered in 1820 by H. Ch. Ørsted
How does the field around a wire look?
The Magnetic Effects of Currents
Hans Christian Ørsted "(1777 - 1851)
Magnetic Field Due to Long Current-Carrying Wire