 Magnetism 10 - Gauss's Law (Magnetism Flavor) ════════════════════ M/c O' the Day: Today's Safari Guide is: Ian! Released Exam Problem ════════════════════ OPENING QUESTION: Starting with Ampere's Law, please derive an equation that shows the B field at some distance away from a solenoid with n coils.       OBJECTIVES:   I will be able to derive an expression relating B field strength to the number of coils in a solenoid during today's class. I will be able to use Gauss's Law in Magnetism to <> during today's class WORDS/FORMULAE FOR TODAY TERMS Magnetic Field (B): A vector value Magnetic Force (FB): Also a vector CONSTANTS:   UNITS: Tesla = T defined as 1 N/C(m/s) FORMULAE: ∮B ∙ ds = μoI: Ampere's Law FB = qv x B FB = qvB FB = qvBsinθ FB = IL x B FB = ∫I ds x B NOTE: AP Version is: FB = ∫I dℓ x B v = E/B τ = IAB (torque in a current carrying loop) τ = NIA x B (torque in a current carrying loop - vector version) τ = μ x B (torque in a current carrying loop - abbreviated version) KE = q2B2R2/2m dB = (μoI/4π)(dℓ x r̂ )/r2 (BS Law) B∮ds = μoI (Ampere's Law) B = μo(N/ℓ)I=μonI Φ =∫B ∙ dA = BAcosθ WORK O' THE DAY:  Gauss revisited: ΦB =∫B ∙ dA = BAcosθ What do you suppose Φ is in this context? Please converse with your crew... Also, what is the significance of the *dot* product here? ════════════════════ Here be Ampere's Law: B∮ds = μoI What is the significance of the ∮integral? How have we used that so far? ════════════════════   Answers: The ∮integral requires use to move around an enclosed area. Up until now we've been talking about a long straight wire. What better shape to use to enclose such a beastie than a ring of radius "r"... that works very, very nicely. But... what if the area we were interested in enclosing was a rectangle(???), would that still work? Let's try: Consider the following sitchation-- A long straight wire is shown some distance away from a rectangular loop of wire as shown: Work with your group to come up with a strategy as indicated... Annotate your steps DO NOT PEEK until you have a strategy to begin, then *carefully* peek if you need additional hints... ════════════════════ COURSEWORK: 30.47 & 30.48 begining on page 930     ANSWERS: STUDY GUIDE: