Electric forces affect only objects with charge

1. Electricity Electric Fields Electric Charge • Electric forces affect only objects with charge • Charge is measured in Coulombs (C). A Coulomb is a lot of charge • Charge comes in both positive and negative amounts • Charge is conserved – it can neither be created nor destroyed • Charge is usually denoted by q or Q • There is a fundamental charge, called e • All elementary particles have charges thatare simple multiples of e Particleq Proton e Neutron 0 Electron -e Oxygen nuc. 8e ++ 2e Red dashed line means you should be able to use this on a test, but you needn’t memorize it

2. Charge Can Be Spread Out • Charge may be at a point, on a line, on a surface, or throughout a volume • Linear charge density  units C/m • Multiply by length • Surface charge density units C/m2 • Multiply by area • Charge density units C/m3 • Multiply by volume

3. The Nature of Matter + + + + + + + + + + + + + + + + • Matter consists of positive and negative charges in very large quantities • There are nuclei with positive charges • Surrounded by a “sea” of negativelycharged electrons • To charge an object, you can add some charge to the object, or remove some charge • But normally only a very small fraction • 10-12 of the total charge, or less • Electric forces are what hold things together • But complicated by quantum mechanics • Some materials let charges move long distances, others do not • Normally it is electrons that do the moving Conductors allow their charges to move a very long distance Insulators only let their charges move a very short distance

4. Some ways to charge objects – – + + – – + + – – – – + + – – + + + + • By rubbing them together • Not well understood • By chemical reactions • This is how batteries work • By moving conductors in a magnetic field • Get to this in March • By connecting them to conductors that have charge already • That’s how outlets work • Charging by induction • Bring a charge near an extended conductor • Charges move in response • Separate the conductors • Remove the charge +

5. Coulomb’s Law • Like charges repel, and unlike charges attract • The force is proportional to the charges • It depends on distance q1 q2 • Other ways of writing this formula • The r-hat just tells you the direction of the force • When working with components, often helps to rewrite the r-hat • Sometimes this formula is written in terms of aquantity0 called the permittivity of free space

6. Forces From Continuous Charges • If you have a spread out charge, it is tempting tostart by calculating the total charge • Generally not the way to go • The charge of the line is easy to find, Q = L • But the distance and direction is hard to find • To deal with this problem, you have to divide it up into little segments of length dl • Then calculate the charge dQ =  dl for each little piece • Find the separation rfor each little piece • Add them up – integrate • For a 2D object, it becomes a double integral • For a 3D object, it becomes a triple integral q r  dl

7. Sample Problem 3.0 mC Three charges are distributed as shown at right. Where can we place a fourth charge of magnitude 3.0 mC such that the total force on the 1.0 mC vanishes?  ? 1.0 mC 2.0 mC 1.0 m 1.16 m 2.0 m -4.0 mC

8. The Electric Field • Suppose we have some distribution of charges • We are about to put a small charge q0 at a point r • What will be the force on the charge at r? • Every term in the force is proportional to q0 • The answer will be proportional to q0 • Call the proportionality constant E, the electric field q0 r The units for electric field are N/C • It is assumed that the test charge q0is small enough that the other charges don’t move in response • The electric field E is a function of r, the position • It is a vector field, it has a direction in space everywhere • The electric field is assumed to exist even if there is no test charge q0 present

9. Electric Field From a Point Charge q q0 • From a single point charge, the electric field is easy to find • It points away from positive charges • It points towards negative charges - +

10. Electric Field from Two Charges • Electric field is a vector • We must add the vector components of the contributions of multiple charges + + + -

11. Electric Fields From Continuous Charges P r • If you have a spread out charge, We can add up the contribution to the electric field from each part • To deal with this problem, you have to divide it up into little segments of length dl • Then calculate the charge dQ =  dl for each little piece • Find the separation r and the direction r-hatfor each little piece • Add them up – integrate • For a 2D object, it becomes a double integral • For a 3D object, it becomes a triple integral  dl

12. Sample Problem • Divide the line charge into little segments • Find the charge dQ =  dx for each piece • Find the separation rfor each little piece • Add them up – integrate P r a  dx x c b What is the electric field at the point P for a line with constant linear charge density  and the geometry sketched above? • Look up integrals

13. Electric Field Lines + • Electric field lines are a good way to visualize how Electric fields work • They are continuous oriented lines showing the direction of the electric field • They never cross • Where they are close together, the field is strong • The bigger the charge, the more field lines come out • They start on positive charges and end on negative charges (or infinity) -

14. Sample Problem Sketch the field lines coming from the charges below, if q is positive • Let’s have four lines for each unit of q • Eight lines coming from red, eight going into green, two coming from blue • Most of the “source” lines from red and blue will “sink” into green • Remaining linesmust go to infinity +2q -2q +q

15. Acceleration in a Constant Electric Field • If a charged particle is in a constant electric field, it is easy to figure out what happens • We can then use all standard formulas for constant acceleration A proton accelerates from rest in a constant electric field of 100 N/C. How far must it accelerate to reach escape velocity from the Earth (11.186 km/s)? • Look up the mass and charge of a proton • Find the acceleration • Use PHY 113 formulas to get the distance • Solve for the distance