Energy Density of Electric Field Energy can be stored in electric fields!u el E one _ plate = ( Q / A) (for small s) 2! 0 (Q / A) F by _ you = QE = Q 2! 0!U electric = F by _ you!s = Q 1 ' Q / A$! U el = ( 0 % " A! s 2 & ( 0 # E Field energy density:! volume (J/m3) ( ) = 1 2 " 0 E 2 (Q / A) 2" 0!s 2 volume 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, W external > 0, is done on the system by you part of the surroundings.!e system =!KE +!U electric = W external If the force exerted by you just offsets the attractive force, F by-plates, so that the plate moves with no gain in KE,!U electric = W external = F by _ 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 Surroundings System 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 Surroundings System e + e - Single charge: 1 E ~ r Dipole: E 2 1 ~ r 3 (far) Energy:! 1 " 0E 2 2 dv Energy stored in the E fields decreases as e + and e - get closer!
An Electron and a Positron Surroundings System e + e - Principle of conservation of energy: Δ(Field energy) + ΔK positron + ΔK electron = 0 Δ(Field energy) = -2(ΔK electron ) Alternative way: e + and e - are both in the system: ΔU el = -2(ΔK electron ) 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 10 16 electrons enter a light bulb in 3 ms what is the magnitude of electron current at that point in the circuit? i N t 16 1.8! 10 = electrons = 6! 10 18 3 3! 10 s = " electrons/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: Use short bulb 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?
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