PHYS 012 1st Edition Lecture 15Outline of Last Lecture II. Induced Currenta. When a conductive object (metal bar, wire, etc.) moves through a magnetic field B, a current is induced in the direction of the magnetic force FB.b. Metal bar through a magnetic fieldc. Bar magnet through a coiled conductive wired. Closed loop inside a circuitIII. Magnetic Flux (ΦB)a. ΦB = ΣBΔAcosθ in T/m2(weber, Wb)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.b. Change in magnetic flux causes an induced currenti. Can be due to change in magnetic field strength (B), area (A), or angle (θ)IV. Faraday’s Lawa. εind = -N(ΔΦB/Δt)b. Problem: Find an expression for Fapp so bar moves at a constant velocity:i. Fapp = FBii. Iind = |εind|/Riii. Φ = ΣBΔAcosθ = BΣΔA = BLy (y is changing)iv. εind = -N(ΔΦB/Δt) = -(ΔBLy)/Δt = -BL (Δy/Δt) = -BLvv. Iind = (-BLv)/Rvi. FB = [(BLv)/R] LBsinθ = (B2L2v)/ROutline of Current Lecture V. Problem: Find the force on the rectangular coil as it enters the magnetic field B at constant velocity v.a. Entering field: flux is increasing induced electromagnetic force (εmf) induced currenti. ΦB = ΣBΔAcosθ = Blyii. εind = -N (ΔΦB/Δt) = -NBL(Δy/Δt) = -NBLviii. Iind = εind/R = -NBLv/R1. Causes forces on sides of coil inside B; forces up and down cancel; net force to the lefiv. Fnet = NILBsinθ = N[(NBLv)/R]LB = (N2B2L2v)/R (to the lef)b. Inside field: no change in flux no εmf or current inducedc. Leaving field: flux decreasing induced εmf induced current in opposite direction as enteringi. Net force also to the lef with same magnitudeVI. Lenz’s Law: the polarity of an induced εmf is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loopa. Ex) Conductive bar moving in a circuit in a magnetic fieldb. Ex) Circuit next to a wire carrying a rapidly decreasing currentc. Ex) Closed loop of wire inside a closed current where switch has just been closedd. Ex) Magnet next to a wire circuit wrapped around a conductive metal
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