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## 27 Electromagnetic Induction Essential University Physics Richard Wolfson In Cha

Wheeler, Patti, Morning Drive-Time On-Air Personality has reference to this Academic Journal, PHwiki organized this Journal 27 Electromagnetic Induction Essential University Physics Richard Wolfson In Chapter 27 you learnt To explain the phenomenon of electromagnetic induction To calculate induced emfs in addition to currents To use energy conservation to find the direction of induced effects To describe important technological applications of induction To explain inductance And describe the role of inductance in simple circuits That magnetic fields store energy And how to calculate that energy To recognize Faradays law as one of the four fundamental laws of electromagnetism And to calculate induced electric fields Electromagnetic induction Electromagnetic induction involves electrical effects resulting from changing magnetic fields. Simple experiments (next slide) show that it doesnt matter how the magnetic field changes: Induced electrical effects occur in all cases of changing magnetic fields. (1) Move a magnet near a circuit; an induced current results. (2) Move the circuit near a magnet; an induced current results. (3) Energize one coil to make it an electromagnet; move it near a circuit in addition to an induced current results. (4) Energize one coil to make it an electromagnet; hold it stationary in addition to move a circuit near itan induced current results. (5) Change the current in one circuit, in addition to thus the magnetic field it produces; an induced current results in a nearby circuit.

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Five simple experiments Experiment 1: moving magnet Experiment 2: moving circuit/coil Experiments 3 in addition to 4: two circuits; either one moving Experiment 5: changing field/current; no motion Faradays law Faradays law, in its simplest as long as m, describes induction by relating the emf induced in a circuit to the rate of change of magnetic flux through the circuit: Here the magnetic flux is given by With a flat area in addition to uni as long as m field, this becomes The flux can change because of changing field B, changing area A, or changing orientation . Moving a magnet near a wire loop increases the flux through the loop. The result is an induced emf given by Faradays law. The induced emf drives an induced current in the loop. Two examples: A changing field The loop has radius r, resistance R, in addition to is in a magnetic field changing at the rate dB/dt. The induced emf is = r2dB/dt in addition to the induced current is I = (r2/R) dB/dt. A changing area The bar slides on the conducting rails, increasing the circuit area at the rate l dx/dt = lv. The induced emf is = Blv, in addition to the induced current is I = Blv/R.

Clicker question What will be the direction of the current in the loop when it first enters the field shown, coming into the field from the left side clockwise counterclockwise Clicker question What will be the direction of the current in the loop when it first enters the field shown, coming into the field from the left side clockwise counterclockwise Direction of the induced current: Lenzs law The direction of the induced emf in addition to current is described by the minus sign in Faradays law. But its easier to get the direction from conservation of energy. The direction of the induced current must be such as to oppose that change that gives rise to it. This is known as Lenzs law. Otherwise we could produce energy without doing any work! Here the north pole of the magnet approaches the loop. So the induced current makes the loop a bar magnet with north to the left, opposing the approaching magnet.

Its the change that matters Lenzs law says that induced effects oppose the changes that give rise to them. Now the induced current flows the opposite way, making the loops south pole to the left in addition to opposing the withdrawal of the magnet. Electric generators Electric generators use a rotating coil in a magnetic field to convert mechanical to electrical energy. Here its the orientation thats changing to produce the changing magnetic flux. Lenzs law makes it hard to turn a generator thats supplying electrical energy. Thats why we have to burn fuels or use the energies of water or wind to generate electricity. Clicker question A copper penny falls on a path that takes it between the poles of a magnet. Does the penny hit the ground going faster or slower than if the magnet were not present The penny will hit the ground going faster. The penny will hit the ground going slower. The penny will hit the ground going the same speed either way.

Clicker question A copper penny falls on a path that takes it between the poles of a magnet. Does the penny hit the ground going faster or slower than if the magnet were not present The penny will hit the ground going faster. The penny will hit the ground going slower. The penny will hit the ground going the same speed either way. Inductance Mutual inductance occurs when a changing current in one circuit results, via changing magnetic flux, in an induced emf in addition to thus a current in an adjacent circuit. Mutual inductance occurs because some of the magnetic flux produced by one circuit passes through the other circuit. Self-inductance occurs when a changing current in a circuit results in an induced emf that opposes the change in the circuit itself. Self-inductance occurs because some of the magnetic flux produced in a circuit passes through that same circuit. Clicker question A long wire carries a current I as shown. What is the direction of the current in the circular conducting loop when I is decreasing The current flows counterclockwise. The current flows clockwise.

Clicker question A long wire carries a current I as shown. What is the direction of the current in the circular conducting loop when I is decreasing The current flows counterclockwise. The current flows clockwise. Self-inductance The self-inductance L of a circuit is defined as the ratio of the magnetic flux through the circuit to the current in the circuit: In differential as long as m: There as long as e, by Faradays law, the emf across an inductor is The minus sign shows that the direction of the inductor emf is such as to oppose the change in the inductor current. Clicker question Current flows from left to right through the inductor as shown. A voltmeter connected across the inductor gives a constant reading, in addition to shows that the left end is positive. Is the current in the inductor changing, in addition to if so, how The current is increasing. The current is decreasing. The current is constant.

Clicker question Current flows from left to right through the inductor as shown. A voltmeter connected across the inductor gives a constant reading, in addition to shows that the left end is positive. Is the current in the inductor changing, in addition to if so, how The current is increasing. The current is decreasing. The current is constant. Magnetic energy As current builds up in an inductor, the inductor absorbs energy from the circuit. That energy is stored in the inductors magnetic field. For an inductor, the stored energy is Considering the uni as long as m magnetic field inside a solenoid shows that the magnetic energy density is This is a universal expression: wherever theres a magnetic field, theres energy with density B2/20. Induced electric fields The induced emf in a circuit subject to changing magnetic flux results from an induced electric field. Induced electric fields result from changing magnetic flux. This is described by the full as long as m of Faradays law, one of the four fundamental laws of electromagnetism: where the integral is taken around any closed loop, in addition to where the flux is through any area bounded by the loop. Loosely, Faradays law states that a changing magnetic field produces an electric field. Thus not only charges but also changing magnetic fields are sources of electric field. Unlike the electric field of a static charge distribution, the induced electric field is not conservative. O

Static in addition to induced electric fields Static electric fields begin in addition to end on charges. But induced electric fields generally as long as m closed loops. Summary Faradays law describes electromagnetic induction, most fundamentally the phenomenon whereby a changing magnetic field produces an electric field: This induced electric field is nonconservative in addition to its field lines have no beginnings or endings. In the presence of a circuit, the induced electric field gives rise to an induced emf in addition to an induced current. Lenzs law states that the direction of the induced current is such that the magnetic field it produces acts to oppose the change that gives rise to it. Self-inductance is a circuit property whereby changing current in a circuit results in an induced emf that opposes the change. Consideration of current buildup in an inductor shows that all magnetic fields store energy, with energy density B2/20. O Magnetic induction in addition to Faradays law Ch 27 Problem 40 A square wire loop with sides of 3.0 m is perpendicular to a uni as long as m magnetic field of 2.0 T. A 6.0 V light bulb is in series with the loop. The magnetic field is reduced steadily to zero over time t. Find t such that the light will shine at full brightness during this time. Which way will the loop current flow

(a) State Faradays law in addition to Lenzs law using words as well as symbols. Explain all symbols that you use. [6] (b) A small circular copper ring is inside a larger loop that is connected to a battery in addition to a switch as shown in the figure. Use Lenzs law to find the direction of the current induced in the small ring just after switch S is closed, after S has been closed a long time in addition to (iii) just after S has been reopened after being closed a long time. [4] Magnetic induction in addition to Faradays law Ch 27 Exercise 18 A conducting loop of area 240 cm2 in addition to resistance 12 lies at right angles to a spatially uni as long as m magnetic field. The loop carries an induced current of 320 mA. At what rate is the magnetic field changing Ch 27 Exercise 19 The magnetic field inside a 20 cm diameter solenoid is increasing at a rate of 2.4 T/s. How many turns should a coil wrapped around the outside of the solenoid have so that the emf induced in the coil is 15 V Both on Sheet 10

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