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.

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

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 a 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 centers.

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 constant 8.99x109 (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, but not including the forces the other two have on each other. Total Force on particle C = Force on C due to A + Force on C due to B F c = F ca + F cb

Electrostatics: Coulomb’s Law The FINDING A cheat-sheet for electrostatics 4  0 = 9.00 × 10 9 Nm 2 /C 2 : q1q1 Point chargeCharge between sheets Charge dipole Potential V or J/Cq 1 /4  0 rVq 1 l cos  /4  0 r Field V/m or J/Cm E = d[v(r)]/dr q 1 /4  0 r 2 V/dq 1 l cos  /4  0 r 2 Force N or J/mq 1 q 2 /4  0 r 2 Coulomb’s law qV/dq 1 q 2 l cos  /4  0 r 2 Work J W = ∫ [F(r)]dr q 1 q 2 /4  0 rqVq 1 q 2 l cos  /4  0 r q2q2 q d

Electrostatics: Coulomb’s Law Electric field ) 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 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:

Working components of a photocopier Photoreceptor drum (or belt) Corona wires Lamp and lenses Toner Fuser Electrostatics: Coulomb’s Law How a photocopier works 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.

Working components of a photocopier Photoreceptor drum (or belt) Corona wires Lamp and lenses Toner Fuser Electrostatics: Coulomb’s Law How a photocopier works For a photocopier to work, a field of positive charges must be generated on the surface of both the 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.

Working components of a photocopier Photoreceptor drum (or belt) Corona wires Lamp and lenses Toner Fuser Electrostatics: Coulomb’s Law How a photocopier works 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 spectrum doesn't have enough gusto 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 old incandescent or fluorescent bulb to flash light onto the original document.

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 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. Working components of a photocopier Photoreceptor drum (or belt) Corona wires Lamp and lenses Toner Fuser Electrostatics: Coulomb’s Law How a photocopier works

Electrostatics: Coulomb’s Law The test!! At a toner-drum distance of 1 cm, how much electrical charge will you need on the toner and drum to lift the particle that distance?