Physics 1202: Lecture 9 Today’s Agenda Announcements: –Lectures posted on: –HW assignments, solutions etc. Homework #3:Homework #3: –On Masterphysics today: due Friday this week –Go to masteringphysics.com Midterm 1: –Friday Oct. 2 –Chaps. 15, 16 & 17.

Today’s Topic : Electric current (Chap.17) Review of –Kirchorff’s rules End of Chap. 17: –RC circuits Chap. 18: magnetism

V R1R1 R2R2 V R1R1 R2R2 Summary Resistors in series –the current is the same in both R 1 and R 2 –the voltage drops add Resistors in parallel –the voltage drop is the same in both R 1 and R 2 –the currents add

Kirchoff's First Rule "Loop Rule" or “Kirchoff’s Voltage Law (KVL)” "When any closed circuit loop is traversed, the algebraic sum of the changes in potential must equal zero." This is just a restatement of what you already know: that the potential difference is independent of path! We will follow the convention that voltage gains enter with a + sign and voltage drops enter with a - sign in this equation. RULES OF THE ROAD:  R1R1  R2R2 I Move clockwise around circuit:  R1R1 R2R2  I   IR 1  IR 2     0 0 KVL:

Kirchoff's Second Rule "Junction Rule" or “Kirchoff’s Current Law (KCL)” In deriving the formula for the equivalent resistance of 2 resistors in parallel, we applied Kirchoff's Second Rule (the junction rule). "At any junction point in a circuit where the current can divide (also called a node), the sum of the currents into the node must equal the sum of the currents out of the node." This is just a statement of the conservation of charge at any given node.

RC 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. IR + Q/C – V = 0 –In this case neither I nor Q are known or constant. But they are related, V a b c R C This is a simple, linear differential equation.

RC Circuits Case 1: Charging Q 1 = 0, Q 2 = Q and t 1 = 0, t 2 = t To get Current, I = dQ/dt Q tt I V a b c R C

RC Circuits c Case 2: Discharging: Q 1 = Q 0, Q 2 = Q and t 1 = 0, t 2 = t To discharge the capacitor we have to take the battery out of the circuit (V=0) To get Current, I = dQ/dt t I Q t V a b c R C

Chapter 9, ACT 1 c Consider the simple circuit shown here. Initially the switch is open and the capacitor is charged to a potential V O. Immediately after the switch is closed, what is the current ? A) I = V O /RB) I = 0 C) I = RCD) I = V O /R exp(-1/RC) We remember the equation for a discharging capacitor, We note that Q max /C = V O At t = 0, exp (0) = 1, so I = V O /R V a b c R C

Electrical Instruments The Ammeter The device that measures current is called an ammeter. Ideally, an ammeter should have zero resistance so that the measured current is not altered. A  I R1R1 R2R2 + -

Electrical Instruments The Voltmeter The device that measures potential difference is called a voltmeter. An ideal voltmeter should have infinite resistance so that no current passes through it. V  R1R1 R2R2 I IvIv I2I2

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 Resistive Electric Circuits A circuit consists of a 12 V battery with internal resistance of 2  connected to a resistance of 10 . The current in the resistor is I, 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 I 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.

Step 1: Focus on the problem Drawing with relevant parameters –Voltmeter can be put a two places  R I I r A What is the question ? –What is I ? –What is V ? –What is P battery ? –What is P R ? –What is P total ? –Comment on the various P’s V V 10  2  12 V

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: R = 10 ,r = 2    = 12 V –Unknown: I, V, P’s

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 I:  - Ir - IR = 0  R I I r A Find V: Find the P’s:

Step 4: solve numerically Putting in the numbers

Step 5: Evaluate the answers Are units OK ? – [ I ] = 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 R »Normal: battery is not ideal: it dissipates energy

Magnetism Magnetic effects from natural magnets have been known for a long time. Recorded 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.

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) Does this remind you of a similar case in electrostatics? You can see this field by bringing a magnet near a sheet covered with iron filings

Magnetic Field Lines of a bar magnet Electric Field Lines of an Electric Dipole

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: NS NNSS In 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)

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 Intrinsic “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.

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? Start with some observations: Empirical facts: a) magnitude:  to velocity of q b) direction:  to direction of q q F v mag

Lorentz Force The force F on a charge q moving with velocity v through a region of space with electric field E and magnetic field B is given by: F x x x v B q  v B q F = 0  v B q F  Units: 1 T (tesla) = 1 N / Am 1G (gauss) = T

Lecture 9, ACT 2 Two protons each move at speed v (as shown in the diagram) toward a region of space which contains a constant B field in the -y-direction. –What is the relation between the magnitudes of the forces on the two protons? (a) F 1 < F 2 (b) F 1 = F 2 (c) F 1 > F 2 1A B x y z 1 2 v v

Circular motion Force is perp. to v  = 90 o so sin  = 1 or F=qvB W=0   K=0 –Kinetic energy not changed –Velocity constant: UCM ! R Work proportional to cos  (recall 1201) –  :angle between F and  x –cos  =0 (perpendicular)

Lecture 9, ACT 3 Cosmic rays (atomic nuclei stripped bare of their electrons) would continuously bombard Earth’s surface if most of them were not deflected by Earth’s magnetic field. Given that Earth is, to an excellent approximation, a magnetic dipole, the intensity of cosmic rays bombarding its surface is greatest at the (The rays approach the earth radially from all directions). A) PolesB) EquatorC) Mid-lattitudes