Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20hittHitt(28 – 1)Chapter 28 Magnetic Fields In this chapter we will cover the following topics: Magnetic field vector Magnetic force on a moving charge Magnetic field lines Motion of a moving charge particle in a uniform magnetic field Magnetic force on a current carrying wire Magnetic torque on a wire loop Magnetic dipole, magnetic dipole moment Hall effect Cyclotron particle acceleratorBrBFrmr3 0 :****** :****** 0 1 : : 0 2 : : 0 3 : : 7 4 :************** :************** 7 5 :************** :************** 11 6 :********************** :********************** 13 7 :************************** :************************** 21 8 :****************************************** :****************************************** 11 9 :********************** :********************** 17 10 :********************************** :********************************** 17 11 :********************************** :********************************** 4 12 :******** :********What is the equivalent resistance between points F and G? Each Resistor is 8 Ω.(A) 2.5 Ω(B) 5.0 Ω(C) 2.0 Ω(D) 4.0 Ω(E) none of theseOne can generate a magnetic field using one of the following methods:Pass a current through a wire and thus form what is knows as an "electromagnet".Use a "permanent" ma What produces a magnetic fieldgnet Empirically we know that both types of magnets attract small pieces of iron. Also if supended so that they canrotate freely they align themselves along the north-southdirection. We can thus say that these magnets create in the surrounding space a " " whichmanifests itself by exerting a magnetic force .We will use the magnetic force to define precicely the magnetic field BBFmagnetic fieldrrvector . Br(28 – 2)The magnetic field vector is defined in terms of the force itexerts on a charge which moves with velocity . We inject the charge in a region where we wish to determine BFq vq BDefinition of B rrrr at random directions, trying to scan all the possible directions.There is one direction for which the force on is zero. Thisdirection is parallel with . For all other directions is nBBF qB Frr rot zeroand its magnitude where is the angle between and . In addition is perpendiculat to the plave definedby and . The magnetic force vector is given by the esinquation:BBBv B Fv BF q vFff=r rrrrr The defining equation is sinIf we shoot a particle with charge = 1 C at rightangles ( 90 ) to with speed = 1m/s and the magnetic force 1 N, then = 1 teslaBBqF q vqB vFv BBff== �== �SI unit of B :rrrBF qv B= �r rrsinBF q vB f=(28 – 3)The vector product of the vectors and is a vector The magnitude of is given by the equation: The direction of is perpendicusilar nc a b a bccc abcf�==The Vector Product of two Vectorsr rr r rrrrto the plane P defined by the vectors and The sense of the vector is given by the : Place the vectors and tail to tail Rotate in the plane P along the shortest ana bca baright hand rulea.b.rrrrrrgle so that it coincides with Rotate the fingers of the right hand in the same direction The thumb of the right hand gives the sense of The vector product of two vectors is also known as bcc.d. rrthe " " productcross(28 – 4)The vector components of vector are given by the equations: ,ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ , , x y z z yx y z x y z x y zc a b a ba a i a j a k b b i b j b k c c i c j c kc= -= + + = + + = + + c = a×bThe Vector Product in terms of Vector Componentsrr rrr rr$$ Those familiar with the use of determinants can use the expres , The order of the two vectors in the cross product is imporsic ct ntonax y zx yy z x x z y y xzz xi j ka b a a ab b ba b a b a b a bb= - ==-��NoteN:ote :$r rr( )a a b=- �rr r(28 – 5)In analogy with the electric field lines weintroduce the concept of magnetic field lines which help visualizethe magnetic field vector without using equations. The relation bBMagnetic Field Lines :retween the magnetic field lines and are: B1. At any point P the magnetic field vector B is tangent to the magnetic field linesrrPPBrmagnetic field line2. The magnitude of the magnetic field vector B is proportional to the density of the magnetic field linesrmagnetic field linesPQPBrQBrP QB B>(28 – 6)The magnetic field lines of a permanent magnet are shownin the figure. The lines pass through the body of the magnetand form loops. This is in contrMagnetic field lines of a permanent magndetclose ast to the electric fieldlines that originate and terminate on elecric charges. The closed magnetic field lines enter one point of the magnetand exit at the other end. The end of the magnet from whichthe lines emerge is known as the of the magnet. The other end where the lines enter is called the of the magnet. The two poles of the magnet cannot beseparated. Together they north polesouth poleform what is known as a " "magnetic dipole(28 – 7)rEFrBFCathodeAnodeEF qE=r rBF qv B= �r rrA cathode ray tube is shwon in the figure. Electrons areemitted from a hot filament known as the "cathode". They are accelerated by a voltage applied between the cathode VDiscovery of the electron :and a second electrode known as the "anode".The electrons pass through a hole in the anode and they form a narrow beam. They hit the fluorescent coating of the right wall of the cathode ray tube where they produce a spot of light. J.J. Thomson in 1897 used a version of this tube to investigate the natureof the particle beam that caused the fluorescent spot. He applied constant electric and magnetic fields in the tube region to the right of the anode. With the fields oriented asshown in the figure the electric force and the magnetic force have opposite directions. By
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