Electric Forces and Fields E & M the electrical nature of matter is inherent in its atomic structure atoms are made up of p+, n, and e- a.k.a Electricity and Magnetism the nucleus has p+ and n surrounding the nucleus are e- in orbitals or shells amount of charge on p+ and e- is the same, 1.6 x 10-19 C Sidebar: electrons actually have wavelengths, λ, - the size of the orbital is determined by a multiple of 1/2 λ (remember the pink string) Frictional forces, like rubbing add charge to an object (and remove it from the other object) There are 2 kinds of charge : + and _ Like charges repel: opposite charges attract The force between charges is long range force & inverse with respect to distance Neutral objects have an equal mixture of + and _ charges. 1
Insulators: materials which hold the electrons in place Conductors: materials which allow the electrons to move freely We will consider statics first -- the electrons can move but we look at them when equilibrium has been reached. We will consider moving charges (currents) next. The electrons are the objects that move -- the protons are too tied in the atom. Charging by Friction Charging by Conduction Some materials have a greater affinity for electrons. When materials of different affinities are rubbed together, some electrons are transferred between them. 2
Charging by Induction Notice from the drawings: The charges that transfer are all negative The transferred charges end up on the surface of the object and are equidistant The number of charges stay the same -- only their locations change -- charge is conserved A charged object can exert a force on a neutral* object. *neutral no charge Coulomb's Law K = 8.99 x 10 9 Nm 2 /C 2 = 9.0 x 10 9 Nm 2 /C 2 q is given in Coulombs direction -- force is repulsive for like charges force is attractive for unlike charges 3
Comments on Coulomb's Law treats charges as if they exist at a single point Two + 10nC charged particles are placed 2.0 cm apart on the x-axis. What is the net force on a +10nC charge midway between them? What would the net force be if the charged particle on the right is replaced with -10nC? the charges are on objects which have mass looks much like Newton's Universal Law of Gravity -- except it can be both attractive and repulsive Charges and Forces Homework: beginning on page 679: 1, 5, 9, 11, 13 Electric Forces Electric Field Homework beginning on page 680: 20, 22, 27, 28, 29, 33 Grade:«grade» Subject: «subject» Date:«date» 4
Field Theory Suppose you had a 1 kg mass at the surface of earth -- what force would it experience? a method to simplify forces acting on an object Interaction is between an object and the field at the objects location Consider Gravity The Force Per Kg would be: Picturing a Field - Gravitational Field Picturing a Field - Electric Field 5
For electric charges, the electric field E, is given by: A positive test charge of 5.0 x 10-6 C is in an electric field that exerts a force of 2.0 x 10-4 N on it. What is the magnitude of the field at the location of the test charge? 40 N/C direction --> the direction of a force on a + test charge What kind of charges would make this field? Field lines are lines of force --- they always go away from + and toward _ Remember -- Ben Franklin thought the + charges moved -- that is why test charges are + So what force would a _ charge experience if it was in the field? 6
What kind of charges would make this field? The strength of the field is proportional to the number of field lines If the lines are closer together then the field is stronger If the lines are further apart then the field is weaker Field of a single charge: Field of a sheet of charge: + Direction: away if q > 0 toward if q < 0 E = Q/ε0A away from positive charge ε0 = 1/(4πK) = 8.85 x 10-12 C 2 /(Nm 2 ) 7
Field of Two Parallel Plates Field of an air cleaner: Two charged plates, 38 cm tall by 20.6 cm deep and separated by 0.900 cm, have charges of -540nC and + 540 nc. What is the electric field between the plates? - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + 1 Rank in order, from most positive to most negative, the charges A to E of these five systems. 2 Charges 1 and 2 exert repulsive forces on each other. q 1 = 4q 2. Which statment is true? A 1 proton B 1 electron C D 17 protons 19 electrons 1,000,000 protons 1,000,000 electrons A B C F 1on2 > F 2on1 F 1on2 = F 2on1 F 1on2 < F 2on1 + + + + + q 2 q 1 E glass ball missing 3 electrons 8
3 Rank in order, from largest to smallest, the electric field strengths E A to E D at points A to D. q r A 2q r B 4 Which of the following is the correct representation of the electric field of two positive charges? A a B b C c D d q C 2q D 2r 2r 5 Where is the field strength the greatest? Conductors in Electric Fields: A A B B C C D D E E Suppose E exists inside the conductor. What would happen? 9
Suppose the conductor has a net + charge -- where will the charges be? We, therefore conclude that E = 0 inside a conductor in static equilibrium. + + + ++ + + These charges have a field, which must be perpendicular to the conductor. Suppose you have a conductor with a net charge of +Q. What net charge will be on the interior edge? Why are computer chips and other electric components which are sensitive to electric fields packaged inside bags made of conducting materials? What will the electric field be inside the hole? 10
Suppose the conductor has a net negative charge, what happens to the field near the pointed end? + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + E = 0 - - - - - - - - - - - - - - - - - - - - 11
Forces on Charges in E fields Under normal circumstances the earth's electric field outdoors near ground level is uniform, about 100 N/C, directed down. What is the electric force on a free electron in the atmosphere? What acceleration does this force cause? F = qe = (1.6 x 10-19C )(100 N/C) = 1.6 x 10-17 N a = F m = 1.6 x 10-17 N 9.1 x 10-31 kg = 1.8 x 1013 m/s 2 Electrophoresis of DNA Force and Torque on a Dipole in a Uniform Field + F - + F + L L τ = τ+ + τ- = F + (L/2) + F - (L/2) = qel 12
When a charge moves in an electric field -- work is done on the charge -- this work changes the energy that the charge has -- its electrical potential energy. The amount of work needed per charge depends only on the field strength and how far the charge is moved. We define this potential for creating potential as the electric potential, V, measured in Volts or Joules/Coulomb. 13
Electric potential is a property of the source charges -- the ones creating the field that the charge q might be put in. If there is a potential difference, V, there will be an electric field, E, the electric field will create a force, F, on charges, q, if they are present, these forces can make the charges move -- giving them energy, U e or K. 1 The electric potentials at points A, B and C are V A = 100 V, V B = 250 V and V C = -125 V. A 3 C charged particle moves from A to B to C. How much does the particles electrical potential energy change between A and C? 3 sig figs please What happens to a + charge as it moves to an area with a lower potential? U e = q V = q(v 2 - V 1 ) if V 2 < V 1 then Ue is negative and the charge has lost potential energy 14
Where did it go? The particle gains kinetic energy -- it sped up! A positive charge speeds up if it moves into a region of lower potential -- it slows down if it moves into a region of higher potential. Energy is conserved K i + qv i = K f + qv f 2 A proton with a speed of 2.00 x 10 5 m/s enters a region of space in which there is an electric potential. What is the proton's speed after it moves through a potential of 100 V? give your answer 3 digits x 10 5 m/s m p = 1.67 x 10-27 kg 3 Suppose the proton is replaced with an electron with the same speed (2.00 x 10 5 m/s). What is the electron's speed after it moves through a potential of 100 V? give your answer 3 digits x 10 5 m/s m e = 9.11 x 10-31 kg 15
The ev An electron Volt [ev] is the amount of energy gained by an electron which moves through a potential of 1 Volt. 4 Atomic particles are often characterized by their kinetic energy in MeV (million electron volts). What is the speed of an 8.7 MeV proton? Give your answer 2 sig fig x 10 7 m p = 1.67 x 10-27 kg Parallel Plate Capacitor V = V + - V - = V C = Ed V = 0 V = V + d V = 0 V = V + x + + E = Q/(ε o A) V = Ex = [Q/(ε o A)]x = [V c /d] x voltage increases linearly with distance inside a PPC 16
Potential of a Point Charge E = Kq/r 2 V = Ed V = Kq/r So, as we have seen when there is a charge there is a field, the field is capable of exerting forces on other charges. The field has the potential of giving energy to such charges. q E V I + _ V Charges respond to this by moving, if a path is available we now move from electrostatics to current electricity A conventional current flows in the direction + charges would move. Because the wire connects two points of different potential, there is an E field, which applies a force to the charges causing them to move. If the potential is maintained the current will continue to flow: V E F 17
A current, I, is defined as the amount of charge passing a point in 1 second, the unit for current is Ampere [A]. Charge is conserved, so within a circuit it follows that current must be conserved as well. I = q/ t 1 A = 1C/s I I 1 I = I 1 + I 2 I 2 Energy is supplied to the current because of the potential in a battery -- chemical reactions cause ions within the battery to separate to the + and _ electrodes of the battery. symbol used for battery in a circuit drawing + + + current flows out of the + terminal and into the _ terminal 18
Batteries in series are like a series of elevators -- increasing the potential of the charges in the current 3v The amount of current which is able to flow depends on the potential and the material through which it flows. We define this property of material to allow current at resistance, R, measured in Ohm's [Ω], 1Ω = 1V/A. This is Ohm's Law. 3v a total of 9 v R = V/I V = IR 3v I R The rate energy is used in a circuit is the power, given by E =V P = IV P = The battery gives energy, E, to the current The resistor removes energy. Ohm's Law is true for many materials. 19
Circuits -- Symbols Resistor Battery To completely understand a circuit we need to know: 1) The potential difference across each element in the circuit. (V) 2) The current through each element in a circuit. (I) Wire Juction Kirchoff's Laws Series Circuit R 1 = 4 Ω 1) ΣI in = ΣI out 2) V loop = ΣV i = 0 i 12 V R 2 = 2 Ω 20
In a series circuit R tot = R 1 + R 2 + R 3 +... Parallel Circuit 12 V R 1 = 4 Ω R 2 = 2 Ω 21
In a parallel circuit, resistors add Combined Circuit R 3 = 3 Ω R tot = (1/R 1 + 1/R 2 + 1/R 3 +...) -1 12 V R 1 = 4 Ω R 2 = 2 Ω page 782 and on: 6, 8, 10, 11, 21 Capacitors Page 1 of E field worksheet due Page 2 -- extra credit (print out your successful trials) Grade: Subject: Date: «grade» +Physics «date» 22
Potential Differences are caused by the separation of charge + + + + + + V = Ed A way to separate charge would be to take some charge from one conductor and put it on another one which is close by recall our discussion of parallel plates. As you remove charge from one plate and put it on the other you end up with opposite and equal charges, +Q & _ Q, on the two plates. The Potential difference, V, created is directly proportional to the charge Q αδv Q = CΔV Charging a capacitor The constant of proportionality is called C, the capacitance of the plate configuration. What would happen here? The unit for capacitance is the farad. 1 farad = 1 F = 1C/V 23
1 A 2.5mF capacitor is connected to a 9.0 V battery. What is the charge on the capacitor? Recall for parallel plates E = Q ε o A & E = ΔV c d so Q ε o A = ΔV c d Rearranging terms: 2 The spacing between the plates of a 2.0mF capacitor is 0.050 mm. What is the surface area of the plates? Q = εoa d Vc 24
3 The spacing between the plates of a 2.0mF capacitor is 0.050 mm. 4 If the potential difference across a capacitor is doubled, its capacitance How much charge would be on this capacitor if it is attached to a 9.0 V battery? A B C Doubles Halves Remains the same Energy and Capacitors It doesn't take much work to put the first charge on the plate of a capacitor, but as more and more charges are moved there the force needed to put the next one there increases. As the force increases the work done in moving a charge increases and the energy stored on the field in the capacitor increased. Because we have a changing force, calculus is required to prove this, but the energy stored is U c = ½QΔV note the similarity to a spring (the force to pull a spring increases with the stretch of the spring). 25
U c = ½QΔV c = ½CV c 2 = ½ Q 2 C 5 How much energy is stored in a 2.0mF capacitor that has been charged to 2000V? This energy is stored in the field. 6 What is the average power dissipation if this capacitor is discharged in 10 ms? 7 The plates of a parallel plate capacitor are connected to a battery. If the distance between the plates in halved, the energy of the capacitor A B C D E Increases, by a factor of 4 Doubles Remains the same Is halved Decreases, by a factor of 4 26
Capacitors in parallel Capacitors in series C1 V C1 C2 V C2 Find the equivalent capacitance of the circuit below. 3.0 mf 12 V 5.0 mf 1.0 mf 27
8 Rank in order, from largest to smallest, the equivalent capacitance Ceq of circuits A to C. A B C D E F A, B, C A, C, B B, A, C B, C, A C, A, B C, B, A A B C 3mF 3mF 3mF 3mF 3mF Simple Circuit Dualing Batteries Series vs Parallel Circuits Direction of Current Compass LED Motor Capicitors Single Large and Small Series Parallel Camera RC Circuits C R Before the switch closes, the capacitor has a charge, Qo and ΔV C = Qo/C C ++++ - - - - I o R Immediately after the switch closes, potential across the capacitor causes a current, I o. Current is a flow of charge, so the current discharges the capacitor. 28
C ++ - - I R At a later time the current has reduced the charge on the capacitor, which reduces the potential difference. This leads to a reduced current, I. How long does it take to discharge the capacitor? C ++++ - - - - I o R Apply Kirchoff's loop law: ΣΔV i = ΔV c + ΔV R = 0 = (ΔV c ) o - I o R = 0 The initial current is I o = ( ΔV c ) o R After some time the current will decrease to: I = I o e -t/ τ ΔV C = (ΔV C ) o e -t/ τ τ = RC I = ΔV c R The change in current is not linear, but an exponential decay. 29
τ is called the time constant and is a characteristic time for the circuit. A large τ implies a slow decay, a small τ a fast decay. After t = 1τ has passed, the current and voltage have dropped to e -1 = 37% of their initial values What is happening now? 9.0 V 1.0 µf 10Ω At t = 0 the switch is moved to the point B. What is the current immediately after the switch is closed? What is the current 25 µs later? B 9.0 V 1.0 µf 10Ω 30
Attachments electric hockey_en.jar Electric Field Hockey Post game.doc E fields.docx