Electromagnetic Induction - P2, week 4
Transcript of Electromagnetic Induction - P2, week 4
Electromagnetic induction • Electromagne,c induc,on is the produc-on of an electric current across a conductor moving through a magne-c field
• Discovered by M. Faraday in 1831
• Moving the magnet (or the coil) produces an induced current • An e.m.f is induced in a coil by moving it rela-ve to a magne-c field
S N
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Electromagnetic induction • Lenz’s Law: the direc-on of the induced current is always so as to oppose the change which causes the current
• The strength of the induced current (or induced e.m.f) depends on: • The number of coils in the wire • How fast the magnet is moving • How strong the magnet used is • And what angle the magnet is moving rela-ve to the wire
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Magnetic 1lux and magnetic 1lux density • Magne,c flux φ : the total number of magne-c field lines passing through a specified area in a magne-c field
• B = magne-c field strength = magne-c flux density
B θ=0°
θ θ=90°
ϕ = BAcos(θ ) Units: Tm2 = Weber (Wb) 3
ε = −dΦdt
Faraday’s Law of electromagnetic induction • For a single coil A = πr2 • For coil with N loops use A = Nπr2
• Magne,c flux linkage Φ = Nφ = NBAcos(θ) = NBπr2 cos(θ) Faraday’s Law: the induced e.m.f in a circuit is equal to the rate of change of flux linkage through the circuit 4
Example a. A narrow coil of 10 turns and area 4 x 10-‐2 m2 is placed in a
uniform magne-c field of flux density 10-‐2 Tesla so that the flux links the turns normally. Calculate the average induced e.m.f in the coil if it is removed completely from the field in 0.5s.
b. If the same coil is rotated about an axis through its middle so that it turns through 60° in 0.2s in the field B, calculate the average induced e.m.f.
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Example The magne-c flux through a coil perpendicular to its plane is varying according to the rela-on Weber. What is the induced current through the coil at t=2s if the resistance of the coil is 3.1Ω?
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Φ = [4t3 + 5t2 +8t + 5]
Direction of induced e.m.f. in moving straight conductor • For a straight conductor moving across a magne-c field, we can get the direc-on of the induced current or e.m.f from Fleming’s right-‐hand rule
• Use right-‐hand rule for induced current or e.m.f • Use le6-‐hand rule for force on a current-‐carrying conductor
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Calculation of e.m.f. in moving straight conductor
e.m.f. ε = Φ/t = BA/t = BSL/t = BvtL/t = BvL • The e.m.f. ε induced in a rod of length L moving with speed v at right angles to a uniform magne-c field B is given by ε = BvL
• Force on a current-‐carrying conductor F = B I L • Work done = energy produced
B
v A
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L
ε, I
F
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FS = εIt→ BILS = εIt→ BILvt = εIt→ BvL = ε
Example A train travels at 30m/s due east. Calculate the induced emf between the ends of a horizontal axle CD of the train which is 1.5m long, assuming the Earth’s magne-c field strength is 6x10-‐5 T and acts downwards at 65° to the horizontal. What is the magnitude of the induced emf? Which end of CD is at a higher poten-al?
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Calculation of e.m.f. in spinning disc • A conduc-ng disk rota-ng in a magne-c field generates an e.m.f.
• If disk completes f revolu-ons per second: A=πr2f • Induced e.m.f. ε = Bπr2f
S
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B
r
v=rω
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Example A circular metallic disc is placed with its plane perpendicular to a uniform magne-c field of flux density B. The disc has a radius of 0.2m and is rotated at 5 revolu-ons per second about an axis through its center perpendicular to its plane. The e.m.f between the center and the rim of the disc is balanced by the p.d. across a 10Ω resistor when carrying a current of 1mA. What is the magne-c field strength?
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Calculation of e.m.f. in a rotating coil • Consider a coil with N turns, each of area A, rota-ng at right angles to a uniform magne-c field B with angular speed ω
B
θ
ω
Side view
• Flux linkage Φ = Nφ = NBAcos(θ)
• But θ=ωt so Φ=NBAcos(ωt) • From Faraday’s Law:
ε = −dΦdt
ε = −NBA ddt(cos(ωt))
ε = NBAω sin(ωt)ε0 = NBAω
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Example If a coil of 800 turns each with area 10-‐2 m2 performs 600 revolu-ons per minute in a magne-c field of flux density 5x10-‐2T what is the maximum value of the induced e.m.f?
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Maxwell’s equations • Gauss’s Law of electricity
• Gauss’s Law of magne-sm
• Faraday’s Law of Induc-on
• Ampere’s Law 14
To Do • Read sec-ons 15.1 and 15.2 from the book [p.278-‐p.285 Electromagne-c induc-on]
• Homework Assignment wk4: ques-ons 14.1, 14.3, 14.5, 14.6, 15.1, 15.3
• Hand it in no later than 4:00pm next Wednesday -‐ LATE WORK WILL NOT BE ACCEPTED
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