Electricity

Static Electricity Charge comes in two forms, which Ben Franklin designated as positive (+) and negative (-). Charge is quantized. The smallest possible stable charge, designated as e, is the magnitude of the charge on 1 electron or 1 proton. A proton has charge of e, and an electron has charge of -e. e is referred to as the “elementary” charge. e = 1.602 x 10-19 coulombs. The coulomb is the SI unit of charge.

Sample Problem A certain static discharge delivers -0.5 coulombs of electrical charge. How many electrons are in this discharge? q = n e n = q/e n = (-0.5 C) / (-1.602 x 10-19 C) n = 3,121,098,626,716,604,245 OR 3.12 x 10 18

Sample Problem 1. How much positive charge resides in two moles of hydrogen gas (H2)? 2. How much negative charge? 3. How much net charge?

Sample Problem The total charge of a system composed of 1800 particles, all of which are protons or electrons, is 31x10-18 C. How many protons are in the system? How many electrons are in the system?

Coulomb’s Law and Electrical Force

Demo #1 1. Demonstrate how you can pick up the tissue without touching it in any way with your body. 2. What is occurring on the atomic level that lets you do this?

The atom The atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction. The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without too much difficulty.

So… You charge the balloon by rubbing it on hair or on a sweater, and the balloon becomes negative. How can it pick up a neutral tissue?

The Electroscope The electroscope is Made from a metal Or other conductor, And may be contained Within a flask. The vanes are free to move.

Demo #2 Rub the plastic rod with the fur. Bring the rod toward the pole of the electroscope. What happens to the vanes? Explain your observations.

Demo #3 Rub the glass rod with the silk. Bring the rod toward the pole of the electroscope. What happens to the vanes? Explain what you observe.

Demo #4 1. What happens when you touch the electroscope with the glass rod?

Electric Force Charges exert forces on each other. Like charges (two positives or two negatives) repel each other resulting in a repulsive force. Opposite charges (a positive and a negative) attract each other, resulting in an attractive force.

Coulomb’s Law - form 1 Coulomb’s law tells us how the magnitude of the force between two particles varies with their charge and with the distance between them. Coulomb’s law applies directly only to spherically symmetric charges.

Coulomb’s Law - form 2

Spherically Symmetric Forces Newton’s Law of Gravity FG = Gm1m2 r2 Coulomb’s Law FE = kq1q2

Sample Problem

Sample Problem

Superposition Electrical force, like all forces, is a vector quantity. If a charge is subjected to forces from more than one other charge, vector addition must be performed. Vector addition to find the resultant vector is sometimes called superposition.

The Electric Field

Gravitational Fields S F = ma GmEmm = ma (2rE) 2 a = G m E 4rE 2

The Electric Field

Why use fields? Forces exist only when two or more particles are present. Fields exist even if no force is present. The field of one particle only can be calculated.

Field around a + charge **The arrows in a field are not vectors, they are “lines of force”. **The lines of force indicate the direction of the force on a positive charge placed in the field. **Negative charges experience a force in the opposite direction.

Field around a - charge

Field between charged plates

Field vectors from field lines The electric field at a given point is not the field line itself, but can be determined from the field line. The electric field vector is always tangent to the line of force at that point. Vectors of any kind are never curved!

Field Lines and Path of Moving Charge The electric field lines do not represent the path a test charge would travel. The electric field lines represent the direction of the electric force on a test particle placed in the field.

Field Vectors from Field Lines

Force from an Electric Field The force on a charged particle placed in an electric field is easily calculated. F = Eq F: Force (N) E: Electric Field (N/C) q: Charge (C)

Sample Problem

Sample Problem

Sample Problem A proton traveling at 440 m/s in the +x direction enters an electric field of magnitude of 5400 N/C directed in the +y direction. Find the acceleration.

For Spherical Electric Fields The electric Field surrounding a point charge or a spherical charge can be calculated by: E = k q / r2 where E: Electric Field (N/C) k: 8.99 x 109 N m2 / C2 q: Charge (C) r: distance from center of charge q (m) Remember that k = 1/4peo

Principle of Superposition When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges. Again, as with force vectors, this is referred to as superposition.

Keep in mind… Electric field lines are NOT vectors, but may be used to derive the direction of electric field vectors at given points. The resulting vector gives the direction of the electric force on a positive charge placed in the field.

Sample Problem A particle bearing -5.0 mC is placed at -2.0 cm and a particle bearing 5.0 mC is placed at 2.0 cm. What is the field at the origin?

Sample Problem

Sample Problem

Electric Potential Energy The energy contained in a configuration of charges. Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable. Unit: Joule

Electric Potential Energy increases when charges are brought into less favorable configurations. DU>0

Electric Potential Energy decreases when charges are brought into more favorable configurations. DU<0

Electric Potential Energy

Work and Charge

Work and Charge

Electric Potential Electric potential is hard to understand, but each to measure. We commonly call it “voltage”, and its unit is the Volt. 1 V = 1 J / C Electric potential is easily related to both the electric potential energy and to the electric field.

Electrical Potential and Potential Energy

Electrical Potential and Potential Energy DV = D U / q

Sample Problem

Electrical Potential in Uniform Electric Fields The electric potential is related in a simple way to a uniform electric field.

Sample Problem

Sample Problem Fr75