Chapter 20 21 Magnetism and Electromagnetism MAGNETISM Arguable

Chapter 20, 21 Magnetism and Electromagnetism

MAGNETISM Arguable the oldest subject in Physics: ancient Greeks (near the City of Magnesia) and Chinese realized certain strange stones attracted iron. Around 1600, William Gilbert proposed that the Earth itself is A gigantic magnet. For a long time, people knew only one source of magnetism from Iron. In 1821, a Danish physicist, Oersted noticed that an electrical wire carrying current made the near-by compass reorient. First clue of inter-relation between electricity and Magnetism. Ampere, Faraday established the nature of electricity and magnetism (all from their experimental observations).

Magnets n Poles of a magnet are the ends where objects are most strongly attracted • Two poles, called north and south n Like poles repel each other and unlike poles attract each other • Similar to electric charges n Magnetic poles cannot be isolated • If a permanent magnetic is cut in half repeatedly, you will still have a north and a south pole • This differs from electric charges • There is some theoretical basis for monopoles, but none have been detected

More About Magnetism n An unmagnetized piece of iron can be magnetized by stroking it with a magnet • Somewhat like stroking an object to charge an object n Magnetism can be induced • If a piece of iron, for example, is placed near a strong permanent magnet, it will become magnetized

S S N N N

S N N S Magnets exist in pairs of N-S poles. A theoretical prediction says that it is possible to have magnetic mono-poles but they have not been observed!! Magnetic field cannot be defined as E-field, FE = q. E F B = q BB

Magnetic Fields n n A vector quantity Symbolized by B Direction is given by the direction a north pole of a compass needle points in that location Magnetic field lines can be used to show the field lines, as traced out by a compass, would look

Magnetic Field Lines, sketch n n A compass can be used to show the direction of the magnetic field lines (a) A sketch of the magnetic field lines (b)

Magnetic Field Lines, Bar Magnet n n Iron filings are used to show the pattern of the magnetic field lines The direction of the field is the direction a north pole would point

Magnetic Field Lines, Unlike Poles n n Iron filings are used to show the pattern of the magnetic field lines The direction of the field is the direction a north pole would point

Magnetic Field Lines, Like Poles n n Iron filings are used to show the pattern of the magnetic field lines The direction of the field is the direction a north pole would point • Compare to the electric field produced by like charges

Magnetic and Electric Fields n n n An electric field surrounds any stationary electric charge A magnetic field surrounds any moving electric charge A magnetic field surrounds any magnetic material

Earth’s Magnetic Field n n The Earth’s geographic north pole corresponds to a magnetic south pole The Earth’s geographic south pole corresponds to a magnetic north pole • Strictly speaking, a north pole should be a “north-seeking” pole and a south pole a “south-seeking” pole

Earth’s Magnetic Field n The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior

S N In unifrom field, no force only torque!!!

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Magnetic Fields n In a magnetic field, a current carrying wire experiences a magnetic force • This force has a maximum value when the wire is perpendicularly to the magnetic field lines • This force is zero when the wire is along the field lines

Magnetic Fields, cont n One can define a magnetic field in terms of the magnetic force exerted on current carrying wire • Similar to the way electric fields are defined

Units of Magnetic Field n The SI unit of magnetic field is the Tesla (T) • Wb is a Weber

B I F FB = ILB Magnetic induction Magnetic flux density Magnetic field (strength) [B] = [F/IL] = Ns/Cm = Tesla *1 Tesla = 104 gauss Length of the section in Bfield

? Magnetic force on a current carrying loop FB = ILB (1) (2) (3) (4) A net force on the loop A net torque on the loop A net force and torque nothing, zip

X X S N

http: //hyperphysics. phy-astr. gsu. edu/hbase/magnetic/mothow. html

DC Electrical Motor X X X X X

Magnetic Force on Moving Charge n n The direction of the magnetic force is always perpendicular to both v and B F = qv. B (v B) Force is smaller when v is not perpendicular to B F = 0 when v is parallel to B

Right Hand Rule n n Hold your right hand open Place your fingers in the direction of B Place your thumb in the direction of v The direction of the force on a positive charge is directed out of your palm • If the charge is negative, the force is opposite that determined by the right hand rule

CRT TV

Nam June Paik http: //www. paikstudios. com/

v x q x x F x Xq x x X x F v X x x qx x x v X x FF q q x x v F = q v B┴ Force by a magnetic field on a moving charge is always Perpendicular to the direction of motion. NO WORK DONE BY THE FIELD!!!

X x X x r x x x v X x x q x m X x x x B FB = q v B Force by B-field This force causes a circular motion. Centrepetal force = FB Fc = mv 2/r = q v B = FB r = mv/q. B Since there is no work done by the field, in vacuum, The charge will make a circular motion forever!!!

Bubble Chamber

B = 0. 36 T r = 0. 4 m Mass m? . . . . A univalent ion with mass m Came into the field region with Speed v = 6 x 105 m/s. Mass spectrometer An object with +e charge And mass m kg

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Magnetic Fields – Long Straight Wire n n A current-carrying wire produces a magnetic field The compass needle deflects in directions tangent to the circle • The compass needle points in the direction of the magnetic field produced by the current

Direction of the Field of a Long Straight Wire n Right Hand Rule #2 • Grasp the wire in your right hand • Point your thumb in the direction of the current • Your fingers will curl in the direction of the field

Magnitude of the Field of a Long Straight Wire n n The magnitude of the field at a distance r from a wire carrying a current of I is µo = 4 x 10 -7 T m / A • µo is called the permeability of free space

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For infinitely long solenoid B = mon. I n: number of turns/m http: //www. bugman 123. com/Physics. html

A solenoid electro-magnet is energized as shown in the figures. Since current flows through wire in the presence of magnetic fields, the solenoid will feel force. Which figure correctly describes the force acting on the solenoid?

Induced emf n A current can be produced by a changing magnetic field • First shown in an experiment by Michael Faraday n n A primary coil is connected to a battery A secondary coil is connected to an ammeter

Faraday’s Experiment n n 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 n n n 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

INDUCTION Michael Faraday (1791 – 1867) …it appeared very extraordinary, that as every electric current was accompanied by a corresponding intensity of magnetic action at right angles to the current, good conductors of electricity, when placed within the sphere of this action, should not have any current induced through them, or some sensible effect produced equivalent in force to such a current.

Primary Coil Secondary coil G ?

Summary of Experimental Findings EMF is induced in the secondary coil Only when the magnetic field through it changes. s ’ z n e w a L EMF induced is bigger if the area of coil is bigger. L EMF is induced always in the opposite direction of change in magnetic field. Vind = - A (d. B/dt) = - d /dt = A B : magnetic flux

Magnetic Flux n n 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 proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loop

B = A B┴ A = (0. 3 x 0. 2)(0. 175 sin(40)) = 0. 06 x 0. 112 = 0. 0067 T. m 2 B = 0. 175 T 40 m B 0. 2 B┴ B// 0. 3 m

+ + - Vind = - d /dt Vt = -3 d /dt Net number of loops Example 23. 2 150 turn loop with a 0. 75 cm 2 cross-section Magnetic field: 0 T 0. 25 T in 3. 6 s 5 Ohm What is the induced current in the coil?

Faraday’s Law and Electromagnetic Induction n n 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 Φ during a time interval t, the average emf induced is given by Faraday’s Law:

Faraday’s Law and Lenz’ Law n The change in the flux, ΔΦ, can be produced by a change in B, A or θ • Since ΦB = B A cos θ n The negative sign in Faraday’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

AC Generator http: //hyperphysics. phy-astr. gsu. edu/hbase/magnetic/motorac. html#c 2

James Clerk Maxwell n n Electricity and magnetism were originally thought to be unrelated in 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena

Maxwell’s Starting Points n n Electric field lines originate on positive charges and terminate on negative charges Magnetic field lines always form closed loops – they do not begin or end anywhere A varying magnetic field induces an emf and hence an electric field (Faraday’s Law) Magnetic fields are generated by moving charges or currents (Ampère’s Law)

Maxwell’s Predictions n n Maxwell used these starting points and a corresponding mathematical framework to prove that electric and magnetic fields play symmetric roles in nature He hypothesized that a changing electric field would produce a magnetic field Maxwell calculated the speed of light to be 3 x 108 m/s He concluded that visible light and all other electromagnetic waves consist of fluctuating electric and magnetic fields, with each varying field inducing the other

Hertz’s Confirmation of Maxwell’s Predictions n Heinrich Hertz was the first to generate and detect electromagnetic waves in a laboratory setting

James Clerk Maxwell’s Equations (1867) E-field comes out from p-charge and Pre-Maxwell terminates at negative charge. B-field cannot do like E-field. No magnetic monopole! Faraday’s law Ampere’s law

The velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments, agrees so exactly with the velocity of light calculated from the optical experiments, that we can scarcely avoid the inference that light consists in the transverse undulation of same medium which is the cause of electric and magnetic Phenomena. 2. 9986 x 108 m/s

Hertz’s Experiment (1887)

Hertz’s Experimental Apparatus n n n An induction coil is connected to two large spheres forming a capacitor Oscillations are initiated by short voltage pulses The inductor and capacitor form the transmitter

Hertz’s Experiment n Several meters away from the transmitter is the receiver • This consisted of a single loop of wire connected to two spheres • It had its own inductance and capacitance n When the resonance frequencies of the transmitter and receiver matched, energy transfer occurred between them

Hertz’s Conclusions n Hertz hypothesized the energy transfer was in the form of waves • These are now known to be electromagnetic waves n Hertz confirmed Maxwell’s theory by showing the waves existed and had all the properties of light waves • They had different frequencies and wavelengths