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PHYS 219 Spring semester 2015 Lecture 14: Faraday’s Law (1831), Lenz’s Law (1835) and Magnetic Induction Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 14 1 Overview In 1831, Faraday discovered that a changing magnetic field creates an electric field This effect is called magnetic induction Faraday’s discovery couples electricity and magnetism in a fundamental way Magnetic induction is the key to MANY technologically relevant inventions. 2 1 Faradays’ Law – Electromagnetic Induction Magnetic flux move magnet thru loop loop with area A B magnetic flux B A a b Eab B t Origin of minus sign is Lenz’s Law 3 Implications Faraday showed that an electric current is produced in a wire loop only when the magnetic field thru the loop is changing A changing magnetic field produces an electric field. 1. An electric field produced in this way is called an induced electric field 2. The phenomena is called electromagnetic induction 4 2 Defining Change in Magnetic Flux with Time x x x x x x x x x x x x x x x x x x x x x x x x Wire loop x x x x x x x x x x x x x x Time =t x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Time =t+Δt x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Time =t Time =t+Δt 5 Faraday’s Law relies on the concept of magnetic flux Magnetic Flux is the product of an area (m2) with a component of a magnetic field (T) passing perpendicularly through it. Convenient to visualize an “area” vector A perpendicular to plane of loop Magnetic flux is similar to the concept of electric flux B ΦB = BA cos(Θ) Θ measures the angle between B and A Units: ΦB = T•m2 = 1 Weber = 1 Wb 6 3 Magnetic Flux is easy to calculate for uniform magnetic fields =3.0 m2 What is the magnetic flux through the surface? =2.0 T =60o ΦB = BA cos(Θ) =2.0 T × 3.0 m2 × cos(60o) =6.0 × 0.5 Tm2= 3 Wb 7 Why cos ? B is a vector! A is to green plane B B// B =Bcos 8 4 Faraday’s Law: An induced emf is produced in a coil whenever the magnetic flux changes with time. Here we focus on an increasing flux through a loop. 2. E is the induced ΔΦB emf that develops E =Δt when the magnetic flux thru the loop 1. B is an external increases with time. applied magnetic This E drives the field that changes current I with time. You control B! 3. I is the induced current that flows due to E Subtle Point: The negative sign indicates that the induced emf is opposite to change in magnetic flux that causes it. Key Idea: An emf is produced by the changing magnetic flux. The emf in turn produces an induced current I. 9 IMPORTANT E B t Minus sign is due to Lenz’s Law Four ways the flux can change: magnitude of B changes with time loop rotates so the angle changes with time w ℓ v B constant but area A changes with time: A=ℓ w where ℓ = v ∆t loop moves from one region to another and magnitude of B field is different 10 5 Example: What is the induced emf if the magnetic field through a six turn coil increases at a rate of 0.17 T/s? E =- The negative sign indicates that the induced emf acts to “oppose” the change in magnetic flux that causes it E=- ΔΦB Δ(B A) ΔB = =A Δt Δt Δt 2 2 A = πR = 0.88 m E = ΔB = +0.17 T / s Δt E =(0.88 m2 )(0.17 T / s) = 0.15 V ΔΦB Δt It is often easier to take the absolute value of Farady’s Law to find the magnitude of the induced emf and then use Lenz’s Law to find the direction of the induced current that results. Since coil has six turns, E = 6 × (0.15 V) = 0.90 V a b 11 Review: You need to know the direction of the magnetic field produced by current in a wire Long straight wire Wire loop I B 12 6 Lenz’s Law There are many ways to state Lenz’s Law. Here is one that makes sense to me: An induced electric current is produced by a changing magnetic field. The induced current will flow in a direction such that it will create its own induced magnetic field that opposes the changing magnetic field that created it. 13 Lenz’s Law – Example 1 I A. Assume a metal loop in which the applied magnetic field (solid arrows) passes upward through it B. Assume the magnetic flux increases with time C. The induced magnetic field produced by the induced current must oppose the change in flux D. Therefore, the induced magnetic field (dotted arrows) must be downward E. The induced current must therefore be clockwise (CW) when viewed from the top of coil 14 7 Lenz’s Law – Example 2 – the dropped magnet The situation when the North pole just enters the loop Be able to distinguish the applied field from the induced field loop An induced current must flow in the loop to produce a magnetic field (inside the loop) that opposes the change in flux. 15 Lenz’s Law – Example 3 - Motion to and from a loop (Focus on the Change in Flux w.Time) a) Iind b) N Steady motion away from loop Iind N Steady motion toward loop loop loop increasing time increasing time The induced current always produces a magnetic field that opposes (counteracts) the change in flux 16 8 Lenz’s Law – Example 4 Jumping Rings Induced magnetic field “PCA – ACR” 17 Up Next – Induced emf 18 9 Appendix Right Hand Rules: Force on moving charge q in B-field Current Loop – direction of B-field at center of loop Current in long straight wire - direction of B-field that curls around the wire Induced current (Lenz’s Law) – direction of current induced by changing magnetic flux Make sure you can distinguish between the different situations 19 Why is Lenz’s Law Confusing? There are four cases to consider for one loop! Bapplied conducting loop Bapplied conducting loop If Bapplied INCREASES with time If Bapplied DECREASES with time If Bapplied INCREASES with time Iinduced Iinduced Iinduced Iinduced CCW CW CW CCW Don’t memorize it – think it through If Bapplied DECREASES with time 20 10 If you like computer simulations, check out Important: Changing magnetic field could also be produced by a 2nd coil https://phet.colorado.edu/sims/faradays-law/faradays-law_en.html 21 11