Electrostatics The study of electric charges

Introduction Did you ever run a comb through your hair? What do you notice. What causes the paper holes to jump onto the comb? There are electrical forces that are in place due to the presence of charge on the comb.

The Atom An atom consists of various charged and uncharged particles. The central region is called the nucleus. Protons (+) and neutrons make up the nucleus. Electrons (-) move around the nucleus in an orbital path. Nucleus Neutrons Protons (+) Electrons (-)

The Significance of Charge As mentioned before, protons are positive and electrons are negative. An atom with balanced charges is considered neutral. The overall charge can be changed by adding or removing electrons. This makes the atom an ion. Overall Charge: (Neutral Atom) (Positive Ion) (Negative Ion) Add e - Take e -

Actual Charge of Protons/Electrons Recall, charge is measured in Coulombs (C). Even though protons and electrons are very small, they still have charge. Let us use q as a variable for charge. Electron Proton

Sample Problem (Atomic Charge) A helium atom has a net electric charge of -8.0x C. Is it neutral or an ion? Are there extra electrons or a shortage of them? How many extra electrons are there? –Charge Per e - : -1.60* C

Sample Problem How many excess electrons are on a ball that has a charge of q = -4x C?

Sample Problem (Atomic Charge) An atom has a net electric charge of 4.8x C. Are there extra electrons or a shortage of them? How many electrons short is this atom? Draw this atom given it is Boron.

Electric Forces Charges exert a force on other charges Like Charges Repel Opposites Attract

Electrostatic Demo’s Tape Electroscope Pith Balls

How do atoms get charged? Work can remove electrons from the atom. –Results in a positively charged atom The free Electron can be transferred to another atom. –Results in negatively charged atoms

Coulomb’s Law The electrostatic force one charged object exerts on an other The force is related to the amount of charge –i.e more charge – more force The force is proportional to 1/d 2 –i.e. the further apart the charges, the smaller the force

Coulomb’s Law SymbolUnit FForceN q1ChargeC q2ChargeC dDistancem KconstantN m 2 / C 2

Ex. Coulomb’s Law Object A has a charge of 6x10 -6 C. Object B has a charge of 3x10 -6 C and is 0.03m away. Calculate the force on A.

Separating Charge Charges are balanced in neutral objects. Work must be done to separate charge (free electrons). Once charge is separated, it can be used in experiments.

Separation of Charge Bring a charge rod near a neutral conductor Like charges are repelled Un-like charges are attracted

Charge by conduction A charge rod touches a neutral conductor Like charges are repelled and uniformly distribute

Charge by Induction A charge object is placed near neutral conductors AB ABABAB Separation of charge takes place Contact between the conducting sphere is broken The charge object is removed The charges on the spheres redistribute to maximum separation Result: Two spheres charged by induction

Charging by Polarization Certain substances, such as the one below, have polar molecules. These molecules have opposite charges at each end. Charging by polarization takes place when a charged object is brought near, realigning the molecules in the substance. Magnification

Conductors and Insulators Electrical Conductors are similar to Heat conductors. Electrical Conductors allow charge to move easily. Electrical Insulators do not allow charge to move easily

Conductors and Insulators Electrical Conductors all electrons to move easily. –Metals –Graphite Electrical Insulators do not allow electrons to move easily –Glass –Plastic –Rubber

Lightning Lightning: An electrical discharge between the clouds and oppositely charged ground. Charging by induction occurs during thunderstorms The negatively charged cloud induces a positive charge on the ground

Lightning Average Temperature30,000 0 C –(roughly 5x as hot as the sun) Typical charge (q) for lightning 10C to 25C How many electrons is this?

Lightning is actually a discharge of static electricity. Charge differences are developed from the friction of dust particles within the cloud. When the concentration of charges becomes too great, an electrical discharge results

Outlet Ground The earth stores a seemingly infinite amount of charge, both kinds. An object is grounded when it is connected to the earth or another large object. Electrical devices often have a “ground,” which prevents unwanted charge buildup. Grounding is also the principle behind lightning rods. Grounding

The Electroscope An electroscope is a device that detects electrical charge in objects brought near. Its metallic inner contents, which are usually neutral, have to be separated from surroundings by some type of insulator. There are two metal leaves that hang inside. When a charged object is brought near, the leaves separate. Charge can also be stored in the electroscope by touching it with the rod. Leaves

Ex. Coulomb’s Law The distance that separates electrons in a typical atom is 1.6E-12m. What is the electrostatic force between them?

Electro-static Applications Electrostatic filter

Ex. Coulomb’s Law Three charges are aligned as shown. Calculate the force on q2 due to q1. Electric Charge Positions Scale: 1 Square = 0.05m q1q1 q3q3 q2q2

Ex. Coulomb’s Law Three charges are aligned as shown. Calculate the force on q 2 due to q 3. Electric Charge Positions Scale: 1 Square = 0.05m q1q1 q3q3 q2q2

Ex. Coulomb’s Law Three charges are aligned as shown. Calculate the force on q2 due to q3. Electric Charge Positions Scale: 1 Square = 0.05m q1q1 q3q3 q2q2

F Net Coulomb’s Law in 2-D To find F net with 3 or more charges Calculate each Force vector. It helps to have a grid system on which to work. Use vector addition to find the resultant F net q2q2 q3q3 q4q4 F 13 F 12 F 14 q1q1

Coulomb’s Law in 2-D (cont.) Find the net force acting on q 1. First find the distance between q 1 and the others. Use the Pythagorean Theorem to find these distances. q2q2 q3q3 q1q1 C A B C B A The variable C from each triangle’s hypotenuse is the variable d used in the Coulomb’s Law equation. 1 st Triangle2 nd Triangle

Coulomb’s Law in 2-D (cont.) q2q2 q3q3 q1q1 Charge (C) q1q1 3.0 X q2q X q3q3 7.2 X F 12 F 13

Coulomb’s Law in 2-D Sample Determine the direction of each of the forces prior to vector addition. q2q2 q3q3 q1q1 5.4N 0.972N hyp opp adj hyp adj opp Quad II Adjust Quad III Adjust F 12 F 13

The remaining task is to use analytical vector addition. Coulomb’s Law in 2-D Sample MagAngXYQ F N146.3° II F N206.6° III F Net 5.94N154.5° II Quad II Adjust

Conclusion Electrostatics, the study of the forces between charges at rest. I had a dream… And in it there’s no lightning

Coulomb’s Law in 2-D Sample Three charges are aligned as shown. Find the net force on q1. Electric Charge Positions Scale: 1 Square = 0.5 cm q1q1 q3q3 q2q2 MagAngXYQ F N146.3° II F N20.6° III F Net 5.94N154.5° II

End Ch 20

Example: Charge Distribution What is the total charge of three conducting spheres with charges of 6q,-1q, and 0q A 6q B -1q C 0q

Example: Charge Distribution cont. What is the final charge distribution if sphere A and B touch? C 0q A 6q B -1q B 2.5q A 2.5q

Example: Charge Distribution cont. What is the final charge distribution if sphere B and C touch? B 2.5q A 2.5q C 0q C 1.25q B 1.25q

Example: Charge Distribution cont. What is the total charge of three conducting spheres A 2.5q C 1.25q B 1.25q

Example: Charge Distribution cont. Sphere B is twice as large as sphere A, what will be the charge distribution after they touch? A 5q B 5q

Charge by Conduction Bring a charge rod near a neutral conductor Like charges are repelled Un-like charges are attracted

A 5q B -1q C 0q

q2q2 q3q3 q1q1 Scale: 1 square =0.1cm

q1q1 q3q3 q2q2