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Announcements WebAssign HW Set 7 due this Friday Problems cover material from Chapters 20 Estimated course grades available on e-learning Office hours: Tea and Cookies with Prof. Kumar, 5 pm today, room 2165 My office hours Th 2-3 pm or make an appointment Always check out for more announcements QUESTIONS? PLEASE ASK!

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**From last time… Ampere’s Law B|| Δℓ = µo I**

Magnetic Field for a long straight wire: Magnetic Force between long straight wires: Magnetic Field of a current loop: Magnetic Field of a solenoid: B = µo n I

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**Induced Voltages and Inductance**

Chapter 20 Induced Voltages and Inductance

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Faraday’s Experiment A current can be produced by a changing magnetic field… When the switch is closed, the ammeter reads a current and then returns to zero When the switch is opened, the ammeter reads a current in the opposite direction and then returns to zero When there is a steady current in the primary circuit, the ammeter reads zero Faraday’s insight: An electrical current is produced by a changing magnetic field The secondary circuit acts as if a source of emf were connected to it for a short time Conclusion: an induced emf is produced in the secondary circuit by the changing magnetic field

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Magnetic Flux emf is induced by a change in the magnetic flux, ΦB, not simply by a change in the magnetic field Magnetic flux is defined in a manner similar to that of electrical flux The flux is defined as ΦB = BA = B A cos θ θ is the angle between B and the normal to the plane The wire is in a magnetic field The loop has an area A SI units of flux are T. m² = Wb (Weber) The value of the magnetic flux is proportional to the total number of lines passing through the loop

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Example Problem 20.16 A circular coil enclosing an area of 100 cm2 is made up of 200 turns of copper wire. The wire making up the coil has a resistance of 5 Ω, and the ends of the wire are connected to form a closed circuit. Initially, a 1.1 T uniform magnetic field points perpendicularly up through the plane of the coil. The direction is then reversed so that the final magnetic field has a magnitude of 1.1 T and points down through the coil. If the time required to reverse directions is 0.10 s, what average current flows through the coil during that time?

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**Electromagnetic Induction and Faraday’s Law**

A current is set up in the circuit as long as there is relative motion between the magnet and solenoid The same experimental results are found whether the loop moves or the magnet moves The current is an induced current because is it produced by an induced emf Faraday’s Law: The instantaneous emf induced in a circuit equals the time rate of change of magnetic flux through the circuit If a circuit contains N tightly wound loops and the flux changes by ΔΦB during a time interval Δt, the average emf induced is given by Faraday’s Law:

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**Faraday’s Law and Lenz’ Law**

ΔΦB, can be produced by a change in B, A or θ Since ΦB = B A cos θ The negative sign in Faraday’s Law is very important, and come about by Lenz’ Law The current caused by the induced emf travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit Example: suppose in the figure, B becomes smaller with time This reduces the flux The induced current will produce an induced field, Bind , in the same direction as the original field

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20.3 Motional EMF Suppose a straight conductor of length ℓ moves perpendicularly with constant velocity through a uniform field The electrons in the conductor experience a magnetic force Recall FM = q v B The electrons move down and pile up at the bottom of the conductor, leaving a net positive charge at the top of the conductor

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**Motional EMF ΔV = E l = B ℓ v**

As a result of this charge separation, an E field (and FE = qE is produced)… Electrons continue to move down until FM = FE q v B = q E E = v B …leading to a potential difference, DV, across the conductor ΔV = E l = B ℓ v The top is at a higher potential

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**Motional EMF in a Circuit**

Now place the conductor on a pair of rails and pull it with an applied force Fapp assume the moving bar has negligible resistance The magnetic force Fapp on the charges sets up an induced current the charges are free to move in the closed path!

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**Motional emf in a Circuit, cont**

The changing magnetic flux through the loop and the corresponding induced emf in the bar result from the change in area of the loop The induced ‘motional’ EMF acts like a battery in the circuit

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Example Problem 20.21 An automobile has a vertical radio antenna 1.20 m long. The automobile travels at a 65.0 km/h on a horizontal road where the earth’s magnetic field is 50.0 μT, directed toward the north and downward at an angle of 65° below the horizontal. (a) Specify the direction the automobile hsould move so as to generate the maximal motional emf in the antenna, with the top of the antenna positive relative to the bottom. (b) Calculate the magnitude of the induced emf.

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Solution to 20.16

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Solution to 20.21

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