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*Chapter 19: Magnetism Magnets Magnets Homework assignment : 18,25,38,45,50 Read Chapter 19...*

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Chapter 19: MagnetismMagnets Magnets Homework assignment : 18,25,38,45,50Read Chapter 19 carefully especially examples.

Magnetic forceMagnets

Magnetic field linesMagnets

Magnetic field linesMagnets

Magnetic field lines (contd)

Magnetic monopole?MagnetsMany searches for magnetic monopolesthe existence of which would explain (within framework of QM) the quantization of electric charge (argument of Dirac)No monopoles have ever been found: Perhaps there exist magnetic charges, just like electric charges.Such an entity would be called a magnetic monopole (having + or magnetic charge).How can you isolate this magnetic charge?Try cutting a bar magnet in half:Even an individual electron has a magnetic dipole!

Magnets Source of magnetic fieldWhat is the source of magnetic fields, if not magnetic charge?Answer: electric charge in motion!e.g., current in wire surrounding cylinder (solenoid) produces very similar field to that of bar magnet. Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter.

Magnets Magnetic field of Earth The geographic North Pole corresponds a magnetic south pole. The geographic South Pole corresponds a magnetic north pole. The angle between the direction of the magnetic field and the horizontal is called the dip angle. The difference between true north and, defined as the geographic North Pole, and north indicated by a compass varies from point to point on Earth. This difference is referred to as a magnetic declination.

Magnetic Fields Magnetic force: Observationsvector productmagnitude:

Magnetic Fields Magnetic force (Lorentz force)SI unit : tesla (T) = Wb/m2right-handrule

Magnetism Magnetic force (contd)Units of magnetic field

Magnetic Fields Magnetic force (Lorentz force)Magnetic force

Magnetic force on a current (straight wire)Magnetic Force on a Current-Carrying Conductor

Magnetic force on a current (straight wire) (contd)Magnetic Force on a Current-Carrying Conductor

Plane of loop is parallel to the magnetic fieldForce and Torque on a Current Loop t=rFsinq

Plane of loop : general caseForce and Torque on a Current Loop

Force and Torque on a Current Loop Plane of loop and magnetic moment

Motor flip the current directionForce and Torque on a Current Loop

Case 1: Velocity perpendicular to magnetic fieldMotion of Charged Particles in a Magnetic Field perpendicular to BThe particle moves at constant speed in a circle in the plane perpendicular to B.F/m = a provides the acceleration to the center, so vRxBF

Case 1: Velocity perpendicular to magnetic field (contd)Motion of Charged Particles in a Magnetic Field

Case 1: Velocity perpendicular to magnetic field (contd)Motion of Charged Particles in a Magnetic Field Velocity selector

Case 1: Velocity perpendicular to magnetic field (contd)Motion of Charged Particles in a Magnetic Field Mass spectrometer

Case 1: Velocity perpendicular to magnetic field (contd)Motion of Charged Particles in a Magnetic Field Mass spectrometer

Case 1: Velocity perpendicular to magnetic field (contd)Motion of Charged Particles in a Magnetic Field Mass spectrometer

Case 1: Velocity perpendicular to magnetic field (cont)Motion of Charged Particles in a Magnetic Field Mass spectrometer

Case 2: General caseMotion of Charged Particles in a Magnetic Field at any angle to B.Begin by separating the two components of into //u//[(u//uu//.u//

Case 2: General case (contd)Motion of Charged Particles in a Magnetic Field Since the magnetic field does not exertforce on a charge that travels in its direction,the component of velocity in the magneticfield direction does not change.

Exercises Exercise 1If a proton moves in a circle of radius 21 cm perpendicular to a B field of 0.4 T, what is the speed of the proton and the frequency of motion?

Exercises Exercise 2Example of the force on a fast moving proton due to the earths magnetic field. (Already we know we can neglect gravity, but can we neglect magnetism?)Let v = 107 m/s moving North.What is the direction and magnitude of F?Take B = 0.5x10-4 T and v B to get maximum effect.(a very fast-moving proton)vxB is into the paper (west). Check with globe

Magnetic field due to a long straight wireIron filingsMagnetic Field of a Long Straight Wire and Amperes LawMagnetic fieldby a long wirem0=4px10-7 T m/Apermeability of free spaceright-handrule 2

Amperes (circular) law : A circular pathAmperes Law Consider any circular path of radius R centered on the wire carrying current I. Evaluate the scalar product BDs around this path. Note that B and Ds are parallel at all points along the path. Also the magnitude of B is constant on this path. So the sum of all the BDs terms around the circle isOn substitution for BAmperes circuital law (valid for any closed path)DsDsDsDsamount of currentthat penetrates theloop

Two parallel wiresForce Between Parallel ConductorsAt a distance a from the wire with current I1 the magnetic field due to the wire is given bydForce per unit length

Two parallel wires (contd)Force Between Parallel ConductorsParallel conductors carrying current in the same direction attract each other. Parallel conductors carrying currents in opposite directions repel each other.dd

Definition of ampereForce Between Parallel ConductorsThe chosen definition is that for d = L = 1m, The ampere is made to be such that F2 = 2107N when I1=I2=1 ampere This choice does two things (1) it makes the ampere (and also the volt) have very convenient magnitudes for every day life and (2) it fixes the size of 0 = 4107. Note 0 = 1/(0c2). All the other units follow almost automatically. d

Magnetic field by a current loopMagnetic Fields of Current Loops and SolenoidsIBDx1Dx2The segment Dx1 produces a magnetic field magnitude B1 at the center of the loop, directed out of the page.2) The segment Dx2 produces a magnetic field magnitude B2 at the center of the loop, directed out of the page. The magnitude of B1 and B2 are the same.RThe magnitude of the magneticfield at the center of a circularloop carrying current IThe magnitude of the magneticfield at the center of N circularloops carrying current I

- If d
The magnetic field of a solenoid is essentially identical to that of a barmagnet Magnetic field by a solenoid (contd)solenoidbar magnetA mystery of :RxPIB field at point P:In a solenoid, the B field at its axis:

placed in