energy density of electric field

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!


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


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


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?


Hans Christian Ørsted "(1777 - 1851)

Magnetic Field Due to Long Current-Carrying Wire

energy density of electric field

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