Chapter 22 Induction
Induced emf A current can be produced by a changing magnetic field First shown in an experiment by Michael Faraday A primary coil is connected to a battery A secondary coil is connected to an ammeter
Faraday s Experiment The purpose of the secondary circuit is to detect current that might be produced by the magnetic field When the switch is closed, the ammeter deflects in one direction and then returns to zero When the switch is opened, the ammeter deflects 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 Conclusions 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 It is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic field
Magnetic Flux The emf is actually induced by a change in the quantity called the magnetic flux rather than simply by a change in the magnetic field Magnetic flux is defined in a manner similar to that of electrical flux Magnetic flux is proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loop
Magnetic Flux, 2 You are given a loop of wire The wire is in a uniform magnetic field B The loop has an area A The flux is defined as Φ B = B A = B A cos θ θ is the angle between B and the normal to the plane
Magnetic Flux, 3 When the field is perpendicular to the plane of the loop, as in a, θ = 0 and Φ B = Φ B, max = BA When the field is parallel to the plane of the loop, as in b, θ = 90 and Φ B = 0 The flux can be negative, for example if θ = 180 SI units of flux are T m² m = Wb (Weber)
Magnetic Flux, final The flux can be visualized with respect to magnetic field lines The value of the magnetic flux is proportional to the total number of lines passing through the loop When the area is perpendicular to the lines, the maximum number of lines pass through the area and the flux is a maximum When the area is parallel to the lines, no lines pass through the area and the flux is 0
Electromagnetic Induction An Experiment When a magnet moves toward a loop of wire, the ammeter shows the presence of a current (a) When the magnet is held stationary, there is no current (b) When the magnet moves away from the loop, the ammeter shows a current in the opposite direction (c) If the loop is moved instead of the magnet, a current is also detected
Electromagnetic Induction Results of the Experiment A current is set up in the circuit as long as there is relative motion between the magnet and the loop The same experimental results are found whether the loop moves or the magnet moves The current is called an induced current because is it produced by an induced emf
Faraday s Law and Electromagnetic Induction 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 ΔΦ during a time interval Δt, the average emf induced is given by Faraday s s Law: ε Φ = N t B
Faraday s Law and Lenz Law The change in the flux, ΔΦ ΔΦ,, can be produced by a change in B, A or θ Since Φ B = B A cos θ The negative sign in Faraday s s Law is included to indicate the polarity of the induced emf, which is found by Lenz Law The polarity of the induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop That is, the induced current tends to maintain the original flux through the circuit
Application of Faraday s Law Motional emf A straight conductor of length l moves perpendicularly with constant velocity through a uniform field The electrons in the conductor experience a magnetic force F = q v B The electrons tend to move to the lower end of the conductor
Motional emf in a Circuit Assume the moving bar has zero resistance As the bar is pulled to the right with velocity v under the influence of an applied force, F, the free charges experience a magnetic force along the length of the bar This force sets up an induced current because the charges are free to move in the closed path
Lenz Law Revisited Moving Bar Example As the bar moves to the right, the magnetic flux through the circuit increases with time because the area of the loop increases The induced current must in a direction such that it opposes the change in the external magnetic flux
Lenz Law, Bar Example, cont The flux due to the external field in increasing into the page The flux due to the induced current must be out of the page Therefore the current must be counterclockwise when the bar moves to the right
Lenz Law, Bar Example, final The bar is moving toward the left The magnetic flux through the loop is decreasing with time The induced current must be clockwise to to produce its own flux into the page
Lenz Law Revisited, Conservation of Energy Assume the bar is moving to the right Assume the induced current is clockwise The magnetic force on the bar would be to the right The force would cause an acceleration and the velocity would increase This would cause the flux to increase and the current to increase and the velocity to increase This would violate Conservation of Energy and so therefore, the current must be counterclockwise
Lenz Law, Moving Magnet Example A bar magnet is moved to the right toward a stationary loop of wire (a) As the magnet moves, the magnetic flux increases with time The induced current produces a flux to the left, so the current is in the direction shown (b)
Lenz Law, Final Note When applying Lenz Law, there are two magnetic fields to consider The external changing magnetic field that induces the current in the loop The magnetic field produced by the current in the loop
Generators Alternating Current (AC) generator Converts mechanical energy to electrical energy Consists of a wire loop rotated by some external means There are a variety of sources that can supply the energy to rotate the loop These may include falling water, heat by burning coal to produce steam
AC Generators, cont Basic operation of the generator As the loop rotates, the magnetic flux through it changes with time This induces an emf and a current in the external circuit The ends of the loop are connected to slip rings that rotate with the loop Connections to the external circuit are made by stationary brushed in contact with the slip rings
AC Generators, final The emf generated by the rotating loop can be found by ε =2 B l v =2 B l sin θ If the loop rotates with a constant angular speed, ω, and N turns ε = N B A ω sin ω t ε = ε max when loop is parallel to the field ε = 0 when when the loop is perpendicular to the field
DC Generators Components are essentially the same as that of an ac generator The major difference is the contacts to the rotating loop are made by a split ring, or commutator
DC Generators, cont The output voltage always has the same polarity The current is a pulsing current To produce a steady current, many loops and commutators around the axis of rotation are used The multiple outputs are superimposed and the output is almost free of fluctuations
Chapter 23 Electromagnetic waves
Electromagnetic Waves Produced by an Antenna When a charged particle undergoes an acceleration, it must radiate energy If currents in an ac circuit change rapidly, some energy is lost in the form of em waves EM waves are radiated by any circuit carrying alternating current An alternating voltage applied to the wires of an antenna forces the electric charge in the antenna to oscillate
EM Waves by an Antenna, cont Two rods are connected to an ac source, charges oscillate between the rods (a) As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = 0 moves away from the rod (b) The charges and field reverse (c) The oscillations continue (d)
EM Waves by an Antenna, final Because the oscillating charges in the rod produce a current, there is also a magnetic field generated As the current changes, the magnetic field spreads out from the antenna
Charges and Fields, Summary Stationary charges produce only electric fields Charges in uniform motion (constant velocity) produce electric and magnetic fields Charges that are accelerated produce electric and magnetic fields and electromagnetic waves
Electromagnetic Waves, Summary A changing magnetic field produces an electric field A changing electric field produces a magnetic field These fields are in phase At any point, both fields reach their maximum value at the same time
Electromagnetic Waves are Transverse Waves The E and B fields are perpendicular to each other Both fields are perpendicular to the direction of motion Therefore, em waves are transverse waves
Properties of EM Waves Electromagnetic waves are transverse waves Electromagnetic waves travel at the speed of light c = µ 1 o ε o Because em waves travel at a speed that is precisely the speed of light, light is an electromagnetic wave
Properties of EM Waves, 2 The ratio of the electric field to the magnetic field is equal to the speed of light E c = B Electromagnetic waves carry energy as they travel through space, and this energy can be transferred to objects placed in their path
Properties of EM Waves, 3 Energy carried by em waves is shared equally by the electric and magnetic fields Average power per unit area = E B 2µ max o max = E 2µ 2 max o c = cb 2µ 2 max o
Properties of EM Waves, final Electromagnetic waves transport linear momentum as well as energy For complete absorption of energy U, p=u/c For complete reflection of energy U, p=(2u)/c Radiation pressures can be determined experimentally
The Spectrum of EM Waves Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengths c = ƒλƒ Wavelengths for visible light range from 400 nm to 700 nm There is no sharp division between one kind of em wave and the next
The EM Spectrum Note the overlap between types of waves Visible light is a small portion of the spectrum Types are distinguished by frequency or wavelength
Notes on The EM Spectrum Radio Waves Used in radio and television communication systems Microwaves Wavelengths from about 1 mm to 30 cm Well suited for radar systems Microwave ovens are an application
Notes on the EM Spectrum, 2 Infrared waves Incorrectly called heat waves Produced by hot objects and molecules Readily absorbed by most materials Visible light Part of the spectrum detected by the human eye Most sensitive at about 560 nm (yellow- green)
Notes on the EM Spectrum, 3 Ultraviolet light Covers about 400 nm to 0.6 nm Sun is an important source of uv light Most uv light from the sun is absorbed in the stratosphere by ozone X-rays Most common source is acceleration of high- energy electrons striking a metal target Used as a diagnostic tool in medicine
Notes on the EM Spectrum, final Gamma rays Emitted by radioactive nuclei Highly penetrating and cause serious damage when absorbed by living tissue Looking at objects in different portions of the spectrum can produce different information