Information for Physics 1201 Midterm I Wednesday, February 20

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1 My lecture slides are psted at Infrmatin fr Physics 1201 Midterm I Wednesday, February 20 1) Frmat: 10 multiple chice questins (each wrth 5 pints) and tw shw-wrk prblems (each wrth 25 pints), giving 100 pints ttal. 2) Clsed bk and clsed ntes. 3) Equatins and cnstants will be prvided n the midterm 4) Cvers the material in Chapters 16, 17, 18, 19, and 20

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3 Chapter 21 Electrmagnetic Inductin

4 Induced Emf and Induced Current S far we have dealt nly with currents and magnetic fields which are cnstant in time, and we have shwn that currents (i.e. mving charges) prduce magnetic fields. Can magnetic fields prduce currents? --> yes, if the magnetic field ging thrugh a lp f wire is changing in time! There are a number f ways a magnetic field can be used t generate an electric current. It is the changing field that prduces the current.

5 Induced Emf and Induced Current The current in the cil is called the induced current because it is brught abut by a changing magnetic field. Since a surce emf (electrmtive frce) is always needed t prduce a current, the cil behaves as if it were a surce f emf. This emf is knwn as the induced emf.

6 Induced Emf and Induced Current An emf can be induced by changing the area f a cil in a cnstant magnetic field In each example, bth an emf and a current are induced because the cil is part f a cmplete circuit. If the circuit were pen, there wuld be n induced current, but there wuld be an induced emf. The phenmena f prducing an induced emf with the aid f a magnetic field is called electrmagnetic inductin.

7 Mtinal Emf THE EMF INDUCED IN A MOVING CONDUCTOR dwnward frce n electrns Each charge within the cnductr is mving and experiences a magnetic frce F = qvb The separated charges n the ends f the cnductr give rise t an induced emf, called a mtinal emf.

8 Mtinal Emf Derive the mtinal emf, E, when v, B, and L are mutually perpendicular Magnetic frce n a charge in the rd F M F M = qvb In equilibrium, the electric frce f repulsin frm charge buildup at the ends, qe (where E is the electric field), balances F M qe = qvb è E = vb Gradient equatin è E = ΔV/Δs = E/L E/L = vb è E = vbl

9 Mtinal Emf Example: Operating a Light Bulb with Mtinal Emf Suppse the rd is mving with a speed f 5.0 m/s perpendicular t a 0.80-T magnetic field. The rd has a length f 1.6 m and a negligible electrical resistance. The rails als have a negligible electrical resistance. The light bulb has a resistance f 96 hms. Find (a) the emf prduced by the rd, (b) the current induced in the circuit, (c ) the electric pwer delivered t the bulb, and (d) the energy used by the bulb in 60.0 s.

10 Mtinal Emf (a) E = vbl = ( 5.0m s)( 0.80 T)( 1.6 m) = 6.4 V E (b) I = E R = 6.4 V 96Ω = A (c ) P = IE = (0.067 A)(6.4 V) = 0.43 W (d) Energy = Pt = (0.43 W)(60.0 s) = 26 J

11 Mtinal Emf MOTIONAL EMF AND ELECTRICAL ENERGY In rder t keep the rd mving at cnstant velcity, the frce the hand exerts n the rd must balance the magnetic frce n the induced current which acts ppsite the directin f F hand F hand = F = ILB Using the numbers frm the last example, F hand = (0.067 A)(1.6 m)(0.80 T) = N and the wrk dne by the hand in 60 s is W hand = F hand x = F hand vt =(0.086 N)(5 m/s)(60 s) = 26 J = Energy

12 Mtinal Emf F The directin f the current in this figure gives an induced frce cnsistent with the cnservatin f energy è the directin f the induced current tends t ppse the applied mtin -- it decelerates the rd nce the applied frce is remved (i.e. it takes energy t light the bulb). The directin f the current in this figure wuld prduce a frce which vilates the principle f cnservatin f energy since it accelerates the rd thus creating energy ut f nthing.

13 Mtinal Emf Cnceptual Example: Cnservatin f Energy A cnducting rd is free t slide dwn between tw vertical cpper tracks. There is n kinetic frictin between the rd and the tracks. Because the nly frce n the rd is its weight, it falls with an acceleratin equal t the acceleratin f gravity. Suppse that a resistance cnnected between the tps f the tracks. (a) Des the rd nw fall with the acceleratin f gravity? (b) Hw des the principle f cnservatin f energy apply?

14 Magnetic Flux RELATIONSHIP BETWEEN MOTIONAL EMF AND MAGNETIC FLUX ( ) ( ) t t BA BA B t t A A B t t L x xl BL t t x x vbl = " " # $ % % & ' = " " # $ % % & ' = " " # $ % % & ' = = E è magnetic flux Φ = BA E In time t 0 an area A 0 is swept ut. In time t an area A is swept ut. t t t Δ ΔΦ = Φ Φ = E The mtinal emf equals the change f the magnetic flux per time E

15 Magnetic Flux GENERAL EXPRESSION FOR MAGNETIC FLUX Φ = BAcsφ è depends n the angle at which the B-field crsses the area Units f magnetic flux: T m 2 = Weber = Wb

16 Magnetic Flux Example. A rectangular cil f wire is situated in a cnstant magnetic field whse magnitude is 0.50 T. The cil has an area f 2.0 m 2. Determine the magnetic flux fr the three rientatins φ = 0, 60, and 90, as shwn. Φ = BAcsφ φ = 0 Φ = (0.50)(2.0)cs 0 = 1.0 Wb φ = 60 φ = 90 Φ = (0.50)(2.0)cs 60 = 0.50 Wb Φ = (0.50)(2.0)cs 90 = 0 Wb

17 Magnetic Flux GRAPHICAL INTERPRETATION OF MAGNETIC FLUX The magnetic flux is prprtinal t the number f field lines that pass thrugh a surface.

18 Faraday s Law f Electrmagnetic Inductin FARADAY S LAW OF ELECTROMAGNETIC INDUCTION The average emf induced in a cil f N lps is E E ) = N ' ( Φ Φ t t SI Unit f Induced Emf: vlt (V) & ΔΦ $ = N % Δt (The mtinal emf-φ relatin we derived is a special case f this.) the minus sign reminds us that the induced emf will ppse the change in Φ à Lenz s Law Faraday s law states that an emf is generated if the magnetic flux changes fr any reasn. Since Φ = BA cs φ, any change f B, A, r φ will induce an emf.

19 Faraday s Law f Electrmagnetic Inductin Example: The Emf Induced by a Changing Magnetic Field A cil f wire cnsists f 20 turns each f which has an area f m 2. A magnetic field is perpendicular t the surface. Initially, the magnitude f the magnetic field is T and 0.10 s later, it has increased t T. Find the average emf induced in the cil during this time. ΔΦ BAcsφ B EE = N = N Δt Δt ( B B % = NAcsφ& # = ' Δt $ = V Acsφ ( )( m ) cs( 0) T T 0.10 s

20 Lenz s Law LENZ S LAW The induced emf resulting frm a changing magnetic flux has a plarity that leads t an induced current whse directin is such that the induced magnetic field ppses the riginal flux change. Reasning Strategy fr applying Lenz s Law t finding the induced current directin 1. Determine whether the magnetic flux that penetrates the cil is increasing r decreasing. 2. Find what the directin f the induced magnetic field must be s that it can ppse the change in flux by adding r subtracting frm the riginal field. 3. Use RHR t determine the directin f the induced current.

21 Lenz s Law Cnceptual Example: The Emf Prduced by a Mving Magnet A permanent magnet is appraching a lp f wire. The external circuit cnsists f a resistance. Find the directin f the induced current and the plarity f the induced emf. Since the applied magnetic field in the lp is increasing and pinting t the right, Lenz s law says an induced current will be created in the lp t try t ppse this change by creating an induced magnetic field t the left.

22 Lenz s Law Cnceptual Example: The Emf Prduced by a Mving Cpper Ring. There is a cnstant hrizntal magnetic field directed int the page in the shaded regin. The field is zer utside the shaded regin. A cpper ring is drpped vertically thrugh the regin. Fr each f the five psitins, determine whether an induced current exists and, if s, find its directin. Is the acceleratin f the ring the same as it drps thrugh the five psitins?

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