8.2 Magnetic Flux and Faraday’s Law of Induction p. 311 Magnetic Flux Magnetic flux, ϕ, is defined as the product of the component of the magnetic field, B, perpendicular to the plane of the coil and the area, A, of the coil. Magnetic Flux ϕ = T B A = BA cos Ɵ Michael Faraday determined that the amount of induced emf for a single coil depends on the rate at which the magnetic flux changes with respect to time: Ɛ = ΔϕΔϕ ΔtΔt Where: Δ ϕ = ϕ 2 - ϕ 1 Units: 1 Tm 2 = Wb (Weber)

8.2 Magnetic Flux and Faraday’s Law of Induction p. 313 Faraday’s Law of Induction For a wire with multiple number of loops, N, the equation for induced emf or potential difference becomes: Ɛ = ΔϕΔϕ ΔtΔt -N-N When a changing magnetic flux causes an emf to be induced, the induced emf in turn produces an induced current. The induced current causes a magnetic field to be induced around it. This induced magnetic field opposes the original magnetic flux that produced the induced emf in the first place. This was first stated by Heinrich Lenz and is really another example of the Conservation of Energy Law. Lenz’s Law: The polarity of the induced emf will always be such that it will produce a current whose magnetic field opposes the changing flux that produced the original emf.

8.2 Magnetic Flux and Faraday’s Law of Induction p. 315 Counter EMF (Back EMF) in a Motor A motor and a generator essentially have the same parts. A motor converts electrical energy into kinetic energy and a generator converts kinetic energy into electrical energy. When a current exists in a motor’s armature, the armature turning in a magnetic field produces an induced emf that opposes the voltage of the source making the motor turn. This is known as counter or back emf and is an example of Lenz’s Law in action. The Counter or Back emf equation is derived form Kirchhoff’s Law: Ɛ b = V AB - IR Where V AB is the terminal voltage of the source.

8.2 Magnetic Flux and Faraday’s Law of Induction p. 316 Transformers (part 1) A transformer is a device specifically designed to alter the voltage in an altering current (AC) circuit. The “adapter” used to charge a cell phone is example of a transformer. The transformer is very efficient at doing what is does do to the lack of moving parts (hence very little friction). It is indispensible when transporting electrical energy over long distances. A transformer has two coils, primary or input coil, and secondary or output coil wrapped around laminated soft iron core as shown in the diagram If AC voltage is applied to the primary coil of the transformer, the AC current will induce a changing magnetic field and therefore a changing magnetic flux. Since the changing flux also acts on the secondary coil, an induced AC current and therefore an induced AC Voltage will be produced on the secondary coil. The time for the changing voltages (primary and secondary) on both coils is the same.

8.2 Magnetic Flux and Faraday’s Law of Induction p. 316 Transformers (part 2) Ɛ p = ΔϕΔϕ ΔtΔt -Np-Np From Faraday’s Laws Ɛ s = ΔϕΔϕ ΔtΔt -Ns-Ns The same change in flux, Δ ϕ, occurs in both coils over the same time period. Therefore: ƐsƐs NsNs NpNp ƐpƐp = If you want to step-up the voltage (higher voltage on the output side) then you will need to have more coils on the secondary than on the primary coil. If you want to step-down the voltage (lower voltage on the output side) then you will need to have fewer coils on the secondary than on the primary coil.

8.2 Magnetic Flux and Faraday’s Law of Induction p. 316 Transformers (part 3) Ideal transformers are 100% efficient and real transformers are almost as efficient (99% or better) which means: E in = E out (Since same time for both sides and P = Et) P in = P out Ɛ p I p = Ɛ s I s (Remember: P = VI) ƐsƐs IpIp IsIs ƐpƐp = NsNs NpNp = Note: Current, I and, Number of turns, N, are inverted.

8.2 Magnetic Flux and Faraday’s Law of Induction p. 316 Transformers (part 3) Ideal transformers are 100% efficient and real transformers are almost as efficient (99& or better) which means: E in = E out (Since same time for both sides and P = Et) P in = P out Ɛ p I p = Ɛ s I s Remember: P = VI) ƐsƐs IpIp IsIs ƐpƐp = NsNs NpNp = Note: Current, I and, Number of turns are inverted.

8.2 Magnetic Flux and Faraday’s Law of Induction p. 316 Long Distance Transmission of Electricity (part 1) Transformers are essential to long-distance transmission of power. The power loss in a conductor depends on the current in the wire and the resistance of the wire (P Loss = I 2 R) The resistance of the wire used in power transmission is set by the type of material used (usually aluminum), cross-sectional area of the wire, and the length of the wire. This is very difficult to change once the transmission wire is set up. The current, however, can be changed due to P = VI. For example the same power would occur whether you have high-voltage, low-current or low-voltage, high-current. For transmission of power it is essential that you use high-voltage, low-current combination. A sample calculation show why this on the next page.

8.2 Magnetic Flux and Faraday’s Law of Induction p. 317 Long Distance Transmission of Electricity (part 2) High-Voltage, Low Current (P = W, R = 5 Ω) Low-Voltage, High Current (P = W, R = 5 Ω) Ɛ = V, I = 10 A P source = x 10 = W (same power at source) P loss = I 2 R = 10 2 x 5 = 500 W P delivered = P source - P loss = = W (99.5 %) Ɛ = 1000 V, I = 1000 A P source = 1000 x 1000 = W (same power at source) P loss = I 2 R = x 5 = W P delivered = P source - P loss = = 0 (No powered delivered!) As can be seen in the sample calculations, high voltage must be used and transformers are the key to changing to high voltages for transmission and then back to low voltages for household use.

8.2 Magnetic Flux and Faraday’s Law of Induction Key Questions In this section, you should understand how to solve the following key questions. Page 314 – Practice Problems #2 Page 315 – Quick Check #1 Page 315 – Quick Check #1, & 3 Page 321 – 322 – Review 8.2 #2,4,5,6 & 8