Lecture 16.1 :! Final Exam Review, Part 2 April 28, 2015 1
Announcements Online Evaluation e-mails should have been sent to you.! Please fill out the evaluation form. May 6 is deadline.! Remember that PHY212 and PHY222 (lab) are separate courses!! Check your scores on Blackboard to make sure there are no errors.! Remember that MidTerm #3 will have 60 points added to what you will currently see in Blackboard.! Final Exam is May 4th (a Monday) from 3-5pm in Watson Theatre. Bring your calculator and up to 4 sheets of notes.! I will be around my office today until ~3pm, and tomorrow in the afternoon (1-4pm), so if you would like to meet with me please try those times.! 2
One More Circuit Problem The circuit shown below is referred to as a Wheatstone bridge, and can be used to measure the value of an unknown resistor s resistance (R x in the figure). The idea is that the values of R 1 and R 3 are known, and the value of R 2 is adjusted until the voltage measured between points C and B, V CB, is zero. The bridge is said to be balanced when this condition is reached. a) Assuming we have balanced the bridge, find an expression for R x in terms of R 1, R 2, and R 3 (only these resistor variables should appear in your expression). Hint: Remember that when V CB reads zero, this means points C and B are equipotential, and no current will flow between C and B. 3
Magnetism Some Properties of Magnets: Magnets have two poles (north and south). Like poles repel, opposites attract. If allowed to rotate, like in a compass, a magnet will align itself in a north-south direction. 4 Some materials are attracted to magnets, some are not.
Magnetic Field of Moving Charges Biot-Savart law written using vector cross product: B point charge = µ 0 4 q v r 2 ˆr The Cross Product: C D = CDsin Direction from right-hand rule. 5
Example Problem 6
Magnetic Field of a Current-Carrying Wire Magnetic Field at a distance d away from a long, straight wire carrying current I (see Example 32.3 for derivation) B wire = µ 0 2 I d Use right-hand rule to determine direction 7
Magnetic Dipoles Notice that a current loop has a directionality. Magnetic field flows in one side, and out through the other, just like a magnet. The current loop is a magnet! 8
Ampere s Law Ampere s Law Independent of the shape of the curve around the current.! Independent of where the current passes through curve.! Depends only on the total current (or changing Electric flux - Maxwell) passing through the area enclosed by the integration path. Ampere-Maxwell Law B d s = µ 0 I through + 0 d e dt 9
Magnetic Force on Moving Charge Magnetic Force also depends on how moving charge s velocity is oriented relative to a magnetic field. 10
Example Problem A proton (charge +e) moves to the left (the -y direction), with ~v =1.0 10 6 m/s, through a magnetic field B=5 Tesla which points into the page (the -x direction): 11
Forces on Current-Carrying Wires F on q = qv B q = I t = I l v F wire = Il B F wire = IlB sin Direction from right-hand rule. 12
Magnetic Flux It is once again useful to introduce the idea of the flux of field (magnetic) passing through a current loop. For a uniform magnetic field m = A B Units of magnetic flux:! 1 weber = 1 Wb = 1 Tm 2 13
Faraday s Law All induced currents are associated with a changing magnetic flux. Two ways flux can change:! 1.Geometry: Loop can expand, contract, or rotate.! 2.Magnetic field can change. E = d m dt = B da dt + A db dt 14
Example Problem 15
Inductors Inductors are devices in circuits that can be used to store energy in magnetic fields (similar to Capacitors storing energy in electric fields). They have interesting behavior when placed in circuits. 1 henry = 1 H 1Wb/A = 1 Tm 2 /A Inductance L I m V L = d m dt = L di dt We choose same sign convention as in resistors...voltage decreases in direction of current flow. 16
Inductors We worked out the potential energy stored in the magnetic field of an inductor: U L = 1 A B 2 2µ 0 We could convert this to an energy density by dividing out the volume of the inductor. This result is actually very general. u B = 1 2µ 0 B 2 Recall for Electric Fields: u E = 1 2 0 E 2 17
Example Problem For the given potential across a 50mH inductor, what is I(t) if I=0.20A at t=0s? 18
Transforming Fields General equation for transforming electric and magnetic fields between two inertial reference frames: 19
Maxwell s Equations 20
Polarization Polarizer removes energy from the incident wave by diminishing it s electric field amplitude. I transmitted = I 0 cos 2 21
Reminders! Final Exam is Monday, May 4th from 3-5pm in Watson Hall.! Bring your 4 sheets of notes and a calculator! 22