P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics

Transcription

1 Electrostatics 1

2 Electrostatics: Coulomb s Law The MAN: Charles Augustin de Coulomb He was born in 1736 in Angoulême, France. He received the majority of his higher education at the Ecole du Genie at Mezieres (sort of the French equivalent of universities like Oxford, Harvard, etc.) from which he graduated in He then spent some time serving as a military engineer in the West Indies and other French outposts, until 1781 when he was permanently stationed in Paris and was able to devote more time to scientific research. Between he published seven memoirs (papers) on physics.

3 Electrostatics: Coulomb s Law The INSTRUMENT: The torsion balance

4 Coulomb s torsion balance and how it works Coulomb used a torsion balance to measure electrostatic force. Inside the balance are two pith balls. One is mounted on the end of a glass rod and is unmovable (red), the other can spin around (blue). When the two pith balls are given an electrostatic charge (charging a plastic rod by rubbing it with fur then touching that rod to the pith ball) the mobile ball will move away from the stationary one if both receive the same charge (positive or negative); or will move towards the unmovable ball, if each is given a different charge. The distance the mobile ball moves is used to measure the electrostatic force. Coulomb was able to measure the torsion on the fiber with the scale near the top of the device and the distance between the balls on the scale wrapped around the base of the jar. He derived da mathematical equation that described the relationship between these two measurements. Coulomb s Law states: The force between two small charged spheres is proportional to the magnitude of either charge and inversely proportional to the square of the distance between ee centers. e

5 Coulomb s law Coulomb s Law: The magnitude of the force between two point charges is proportional to the product of their charges and inversely proportional to the square of their separation. 0 = x C 2 N 1 m 2 electric permittivity 2 k = x 10 9 C 2 Nm 2 k = 1/4π 0 Measured charge on the electron: e = 1.6 x C

6 Coulomb s Law Formula Where F is the force between the two particles a and b, q a and q b are the charges on particles a and b, r is the distance between a and b, and k is the Coulomb s constant 8.99x10 9 (Nm 2 /C 2 ). If you have more than two charged particles the force on one would be the sum of the forces acting on it due to the other two particles, il but not including the forces the other two have on each other. TtlF Total Force on particle C = Force on C due to A + Force on C due to B F c = F ca + F cb

7 Electric Field The electric force is a field force, it applies force without touching (like the gravitational force) In the region around a charged object, an Electric Field is said to exist

8 Electric Field Rules for Drawing Electric Field ildlines 1. The lines must originate on a positive charge (or infinity) and end on a negative charge (or infinity). 2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. 3. No two field lines can cross each other. 4. The line must be perpendicular to the surface of the charge

9 Electric field Electric Field Space surrounding an electric charge (an energetic aura) Describes electric force Around a charged particle obeys inverse square law Force per unit charge

10 Electric Field Electric field direction Same direction as the force on a positive charge Opposite direction to the force on an electron

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15 E F E q 0 Electric Field E k q becomes c r 2 E electric field strength, N/C VECTOR q 0 + test charge, C q charge producing field, C r distance between charges, m F E Electric Force, N VECTOR k c coulomb constant, 8.99x10 Nm /C

16 E Field vs g field E Field g field E F 0 q 0 g q 0 F g 0 m 0

17 Coulomb s Law Differences between gravitational and electrical forces Electrical forces may be either attractive or repulsive. Gravitational forces are only attractive.

18 E Field E q r 2 r ˆ

19 Electric Potential Electric potential energy Energy possessed by a charged particle due to its location in an electric field. Work is required to push a charged particle against the electric field of a charged body.

20 Electric Potential (a) The spring has more elastic PE when compressed. (b) The small charge similarly has more PE when pushed closer to the charged sphere. In both cases, the increased PE is the result of work input.

21 Electric Potential Electric potential (voltage) Energy per charge possessed by a charged particle due to its location May be called voltage potential energy per charge In equation form: Electric potential electric potential energy amount of charge

22 Electric Potential Electric potential (voltage) (continued) Unit of measurement: volt, 1 volt 1 joule 1 coulomb Example: Twice the charge in same location has twice the electric potential energy but the same electric potential. 3 times the charge in same location has 3 times the electric potential energy but the same electric potential (2 E/2 q = 3 E/3 q = V)

23 Electric Potential Electric potential (voltage) (continued) High voltage can occur at low electric potential energy for a small amount of charge. High voltage at high electric potential energy occurs for lots of charge.

24 Electric Energy Storage Electrical energy can be stored in a common device called a capacitor. The simplest capacitor is a pair of conducting plates lt separated tdby a small distance, but not touching each other. When the plates are connected to a charging device, such as the battery, electrons are transferred from one plate to the other.

25 Electric Energy Storage This occurs as the positive battery terminal pulls electrons from the plate connected to it. These electrons, in effect, are pumped through the battery and through the negative terminal to the opposite plate. Thecapacitor plates then have equal and opposite charges: The positive plate connected to the positive battery terminal, and The negative plate connected to the negative terminal.

26 Electric Energy Storage The charging process is complete when the potential difference between the plates equals the potential difference between the battery terminals the battery voltage. The greater the battery voltage, and the larger and closer the plates, the greater the charge that can be stored. The energy stored in a capacitor comes from the work required to charge it. Discharging i a charged capacitor can be a shocking experience if you happen to be the conducting path.

27 Electric Energy Storage A common laboratory device for producing high voltages and creating static electricity is the Van de Graaff generator.

28 Conductors in Electrostatic Equilibrium 1. The electric field is zero everywhere inside id a conductor. 2. Any excess charge on an isolated conductor resides entirely on the outside surface of the conductor. 3. Theelectric electric field just outside the charged conductor is perpendicular to the conductor s surface. 4. On an irregularly shaped conductor, charge tends to accumulate where the radius of curvature is the smallest, i.e. AT SHARP POINTS.

29 Electrostatics: Coulomb s Law Electric field 1) Imagine a single charged particle. Charged particles around it will either move directly toward it or directly away from it. In this way, we illustrate t the electric field lines as emanating radially from the charged particle. 2) Imagine a sheet of charged particles: the E field will be perpendicular to the surface. Charged particles and force fields : Electric fields: i / tilit /d / l t i ld/el t i ld

30 Electrostatics: Coulomb s Law How a photocopier works Working components of a photocopier Photoreceptor drum (or belt) Corona wires Lamp and lenses Toner Fuser A drum is basically a metal roller covered by a layer of photoconductive material. This layer is made out of a semiconductor such as selenium, germanium or silicon. What makes elements like selenium so cool is that they can conduct electricity in some cases, but not in others. In the dark, the photoconductive layer on the drum acts as an insulator, resisting the flow of electrons from one atom to another. But when the layer is hit by light, the energy of the photons liberates electrons and allows current to pass through! These newly freed electrons are what neutralizes the positive charge coating the drum to form the latent image.

31 Electrostatics: Coulomb s Law How a photocopier works Working components of a photocopier Photoreceptor drum (or belt) Corona wires Lamp and lenses Toner Fuser For a photocopier to work, a field of positive charges must be generated on the surface of both ththe drum and the copy paper. These tasks are accomplished by the corona wires. These wires are subjected to a high voltage, which they subsequently transfer to the drum and paper in the form of static electricity. One of these wires is stretched parallel to the drum surface and charges the photoconductive surface with positive ions, and the other wire is positioned to coat the paper's surface as the paper shoots by on its way to the drum.

32 Electrostatics: Coulomb s Law How a photocopier works Working components of a photocopier Photoreceptor drum (or belt) Corona wires Lamp and lenses Toner Fuser Making a photocopy requires a light source with enough energy to boot electrons out of the semiconductive coating on the drum (also called a photoconductor, is this case). What wavelengths of light can do this? It turns out that most of the visible spectrum of light contains enough energy to drive the process, especially the green and blue end of the spectrum. Anything lower than the red portion of the visible iibl spectrum doesn't have enough energy to activate the photoconductor. And, although UV light has more than enough firepower to make a photocopy, it can be very damaging to our eyes and skin. This is why photocopiers use a plain li old incandescent or fluorescent bulb lbto flash light onto the original document.

33 Electrostatics: Coulomb s Law How a photocopier works Working components of a photocopier Photoreceptor drum (or belt) Corona wires Lamp and lenses Toner Fuser Toner is sometimes referred to as dry ink, but toner isn't actually ink at all! Ink is a pigmented liquid. Toner is a fine, negatively charged, plastic based powder. The black color in photocopier toner comes from pigments blended into the plastic particles while they aebe are being made. Toner is stuck on larger, positively charged beads and stored inside a toner cartridge. When toner coated beads are rolled over the drum, the toner particles find the positively charged ions on the unexposed areas on the drum's surface attractive. The same particles are subsequently even more drawn to the electrostatically charged paper. The plastic in the toner lets you keep it from jumping ship once you've finally got it on the paper; all you have to do is apply heat to the toner, and the plastic particles melt and fuse the pigment to the paper.

34 Xerography: uses photoconductive material coating(selenium) a drum

35 Millikan Oil-Drop Experiment

36 Millikan Oil-Drop Experiment Robert Millikan measured e, the charge of the electron e = 1.60 x C He also demonstrated the quantized nature of He also demonstrated the quantized nature of this charge

37 Oil-Drop Experiment With no electric field between the plates: The drop reaches terminal velocity with F D = mg

38 Oil-Drop Experiment When an electric field is set up between the plates the drop moves upwards and reaches a new terminal velocity F e = mg +F D =qe Solve for q Solve for q Observed thousands of times and always found e=multiple of 1.6x10 19 C