 EM 02 - Motional EMF A charge is defined to be _____________? A _________________ surounds a charge at ever decreasing distances. A charge can be *ahem* encouraged to move by the presence of __________. A moving charge produces a ____________________. The ________________ is defined to be the number of magnetic field lines present per unit area. Changing _______________ per unit time results in _______________. OPENING QUESTION: What is Faraday's Law? What is the magnetic flux? Why is the change in magnetic flux soooooooooooooooooo important to our day to day life? OBJECTIVES: I will be able to utlize Lenz's Law to PREDICT changes in magnetic fields after today's class. WORDS/FORMULAE FOR TODAY TERMS Inductance Magnetic Flux (ΦB) Magnetic Field (B): A vector value Magnetic Force (FB): Also a vector CONSTANTS:   UNITS: Tesla = T defined as 1 N/C(m/s) FORMULAE: ε = -dΦB/dt ΦB = ∫B ∙ dA ∮B ∙ ds = μoI: Ampere's Law dB = (μoI/4π)(ds x r̂ )/r2 (note r̂ here is the unit vector r̂ like i, j, or k. Biot-Savart Law FB = ∫I ds x B NOTE: AP Version is: FB = ∫I dℓ x B v = E/B FB = qv x B (vector value) FB = qvBsinθ (FB magnitude of only) FB = IL x B WORK O' THE DAY: If you weren't here in class please work this step by step... please do NOT jump ahead (answers are in red bold font) ════════════════════ Consider the following situation of a bar made of some sort of conducting material moving through a magnetic field as shown: Find the weasel word here   (that would be conducting) What does that mean, what are the implications?   (implications are that electrons are free to roam) What will happen to the electrons in the rod? Write the equation that governs that situation.     (Since a B field is perpindicular into the page, the electrons will be pushed to the bottom of the rod) Sketch the situation that now exists.   ════════════════════ Now please work with your group to go step by step through the following... no peeking or jumping ahead PLEASE! Hmmm.... now we have a VERY (I hope!) familiar situation (hint: think about our units immediately following charge).     INDEED!! We have negative charges pulled to the bottom, positive charges pushed to the top and we have the makings of a basic Efield... yay! Please write the equation that shows the FE present here. Soooo.... recollecting that nature ain't all that fond of overabundance, what might you expect the FB and FE to do to the remaining charges in the rod?     YAY!!!! Equilibrium so: FB = FE Substituting our equations from above: qvB = qE Canceling and rearanging we get: qvB = qE Which is a nice equation to have under your belt... Now please work with your group to use that to derive an equation for the electric potential in that situation: Start with basic equation for electric potential: ∆V = Ed but d = ℓ here so: ∆V = Eℓ Recall our working equation: vB =E Substitute for vB for E: ∆V = Bℓv Yay... Soooo... what's that mean? Work with your crew to write a concluding statement.   Now imagine that self-same bar as part of a circuit as shown below: Predict the direction of the current that will be induced to flow in that circuit.       Now please derive an expression for the current present in that situation as sketched below (in terms of current values): Hopefully that yielded: Starting with Ohm's Law: V = IR I = V/R Recalling from work above that: V = Bℓv Substituting for V I = Bℓv/R Now please begin with Newton's Laws, find the velocity of the bar as a function of time (Do I smell... DIFF EQ'S???? HECK YES!)   Hint: the force in the Fx direction is none other than FB   ════════════════════ Fx = ma FB = IℓB ════════════════════ a=dv/dt Check your work from here on page 942. STUDY GUIDE: