Energy Density of Electric Field
Energy can be stored in electric fields
Eone _ plate
Q / A)
(
=
2! 0
Fby _ you = QE = Q
(for small s)
(Q / A)
2! 0
!U electric = Fby _ you !s = Q
(Q / A)
!s
2" 0
2
1 'Q / A$
"" A!s
!U el = ( 0 %%
2 & (0 #
volume
E
!U el
1
2
=
"
E
3)
0
Field energy density: ! volume
(J/m
(
) 2
Energy expended by us was converted into energy stored in the electric field
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 + !U electric = Wexternal
If the force exerted by you just offsets the attractive force,
Fby-plates, so that the plate moves with no gain in KE,
!U electric = Wexternal = Fby _ you !s
Potential Energy and Field Energy
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
An Electron and a Positron
System
Surroundings
e+
e-
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
System
Surroundings
e+
Single charge:
1
E~ 2
r
eEnergy:
1
2
"
E
! 2 0 dV
Dipole:
E~
1
(far)
3
r
Energy stored in the E fields decreases as e+ and e- get closer!
An Electron and a Positron
System
Surroundings
e+
e-
Principle of conservation of energy:
Δ(Field energy) + ΔKpositron + ΔKelectron = 0
Δ(Field energy) = -2(ΔKelectron )
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
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. Magnetic Field
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
Electron Current
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
Both are proportional to the electron current
Exercise
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?
N 1.8 ! 1016 electrons
18
i= =
=
6
!
10
electrons/s
"3
t
3 ! 10 s
Simple Circuits
Thinner
filament wire
Tungsten filament
Inert gas
Use socket
Detecting Magnetic Fields
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?
Compass needle:
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
The Magnetic Effects of Currents
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
Current-Carrying Wire & Compass
The Magnetic Effects of Currents
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?
Hans Christian Ørsted "
(1777 - 1851)
Magnetic Field Due to Long
Current-Carrying Wire