Physics 1402: Lecture 12 Today s Agenda Announcements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW assignments, solutions etc. Homework #4: On Masterphysics : due next Friday at 8:00 AM Go to masteringphysics.com Midterm 1: next week (Oct. 5) Covers Ch. 21-26 esistors in series the current is the same in both 1 and 2 the voltage drops add Summary V 1 esistors in parallel the voltage drop is the same in both 1 and 2 the currents add V 2 1 2 1
ε 1 3 1 ε 2 2 ε 3 C Circuits Consider the circuit shown: What will happen when we close the switch? Add the voltage drops going around the circuit, starting at point a. V a C b c + Q/C V = 0 n this case neither nor Q are known or constant. But they are related, This is a simple, linear differential equation. 2
C Circuits Case 1: Charging Q 1 = 0, Q 2 = Q and t 1 = 0, t 2 = t V a C b c To get Current, = dq/dt Q t t C Circuits Case 2: Discharging To discharge the capacitor we have to take the battery out of the circuit a C b c To get Current, = dq/dt Q t t 3
Chapter 12, ACT 1 Consider the circuit at right after the switch is closed i) What is the initial current? A) 0 B) 1 A C) 2 A D) 3 A E) 4 A 12 V 6 Ω 6 Ω 12 µf ii) What is the current after 2 minutes? A) 0 B) 1 A C) 2 A D) 3 A E) 4 A Lecture 12, ACT 2 f = 3.0 kω, C = 6.0 nf, ε 1 = 10.0 V, Q = 18 nc, ε 2 = 6.0 V, and = 5.0 ma, what is the potential difference V b V a? a. 13 V b. +28 V c. +13 V d. 28 V e. +2.0V 4
Electrical nstruments The Ammeter The device that measures current is called an ammeter. 1 2 - A + ε deally, an ammeter should have zero resistance so that the measured current is not altered. Electrical nstruments The Voltmeter The device that measures potential difference is called a voltmeter. 2 1 2 v ε V An ideal voltmeter should have infinite resistance so that no current passes through it. 5
Problem Solution Method: Five Steps: 1) Focus on the Problem - draw a picture what are we asking for? 2) Describe the physics - what physics ideas are applicable - what are the relevant variables known and unknown 3) Plan the solution - what are the relevant physics equations 4) Execute the plan - solve in terms of variables - solve in terms of numbers 5) Evaluate the answer - are the dimensions and units correct? - do the numbers make sense? Example: Power in esistive Electric Circuits A circuit consists of a 12 V battery with internal resistance of 2 Ω connected to a resistance of 10 Ω. The current in the resistor is, and the voltage across it is V. The voltmeter and the ammeter can be considered ideal; that is, their resistances are infinity and zero, respectively. What is the current and voltage V measured by those two instruments? What is the power dissipated by the battery? By the resistance? What is the total power dissipated in the circuit? Comment on these various powers. 6
Step 1: Focus on the problem Drawing with relevant parameters Voltmeter can be put a two places V What is the question? What is? What is V? What is P battery? What is P? What is P total? Comment on the various P s V r ε 2 Ω 12 V 10 Ω A Step 2: describe the physics What concepts are relevant? Potential difference in a loop is zero Energy is dissipated by resistance What are the known and unknown quantities? Known: = 10 Ω,r = 2 Ω, ε = 12 V Unknown:, V, P s 7
Step 3: plan the solution What are the relevant physics equations? Kirchoff s first law: Power dissipated: For a resistance Step 4: solve with symbols Find : ε - r - = 0 Find V: r ε Find the P s: A 8
Step 4: solve numerically Putting in the numbers Step 5: Evaluate the answers Are units OK? [ ] = Amperes [ V ] = Volts [ P ] = Watts Do they make sense? the values are not too big, not too small total power is larger than power dissipated in» Normal: battery is not ideal: it dissipates energy 9
Magnetism The Magnetic Force B x x x x x x x x x x x x v x x x x x x F q B v q F B v q F = 0 Magnetism Magnetic effects from natural magnets have been known for a long time. ecorded observations from the Greeks more than 2500 years ago. The word magnetism comes from the Greek word for a certain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece or maybe it comes from a shepherd named Magnes who got the stuff stuck to the nails in his shoes Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched. Small sliver of lodestone suspended with a string will always align itself in a north-south direction. ie can detect the magnetic field produced by the earth itself. This is a compass. 10
Bar Magnet Bar magnet... two poles: N and S Like poles repel; Unlike poles attract. Magnetic Field lines: (defined in same way as electric field lines, direction and density) You can see this field by bringing a magnet near a sheet covered with iron filings Does this remind you of a similar case in electrostatics? Electric Field Lines of an Electric Dipole Magnetic Field Lines of a bar magnet 11
Magnetic Monopoles One explanation: there exists magnetic charge, just like electric charge. An entity which carried this magnetic charge would be called a magnetic monopole (having + or - magnetic charge). How can you isolate this magnetic charge? Try cutting a bar magnet in half: S N S N S N n fact no attempt yet has been successful in finding magnetic monopoles in nature. Many searches have been made The existence of a magnetic monopole could give an explanation (within framework of QM) for the quantization of electric charge (argument of P.A.M.Dirac) 12
Source of Magnetic Fields? What is the source of magnetic fields, if not magnetic charge? Answer: electric charge in motion! eg current in wire surrounding cylinder (solenoid) produces very similar field to that of bar magnet. Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter. Orbits of electrons about nuclei ntrinsic spin of electrons (more important effect) Forces due to Magnetic Fields? Electrically charged particles come under various sorts of forces. As we have already seen, an electric field provides a force to a charged particle, F = qe. Magnets exert forces on other magnets. Also, a magnetic field provides a force to a charged particle, but this force is in a direction perpendicular to the direction of the magnetic field. 13
Definition of Magnetic Field Magnetic field B is defined operationally by the magnetic force on a test charge. (We did this to talk about the electric field too) What is "magnetic force"? How is it distinguished from "electric" force? q Start with some observations: CT deflection Empirical facts: a) magnitude: to velocity of q v Fmag b) direction: to direction of q 14