28 - (28 – 1) Chapter 28 Magnetic Fields In this chapter...

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Unformatted text preview: (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 accelerator B r B F r μ r One 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 field gnet Empirically we know that both types of magnets attract small pieces of iron. Also if supended so that they can rotate freely they align themselves along the north-south direction. We can thus say that these magnets create in the surrounding space a " " which manifests itself by exerting a magnetic force . We will use the magnetic force to define precicely the magnetic field B B F magnetic field r r vector . B r (28 – 2) The magnetic field vector is defined in terms of the force it exerts on a charge which moves with velocity . We inject the charge in a region where we wish to determine B F q v q B Definition of B r r r r at random directions, trying to scan all the possible directions. There is one direction for which the force on is zero. This direction is parallel with . For all other directions is n B B F q B F r r r ot zero and its magnitude where is the angle between and . In addition is perpendiculat to the plave defined by and . The magnetic force vector is given by the e sin quation: B B B v B F v B F q v F φ φ = r r r r r r The defining equation is sin If we shoot a particle with charge = 1 C at right angles ( 90 ) to with speed = 1m/s and the magnetic force 1 N, then = 1 tesla B B q F q v q B v F v B B φ φ = = = = SI unit of B: r r r B F qv B = r r r sin B F q vB φ = (28 – 3) The vector product of the vectors and is a vector The magnitude of is given by the equation: The direction of is perpendicu si lar n c a b a b c c c ab c φ = = The Vector Product of two Vectors r r r r r r r r to 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 an a b c a b a right hand rule a. b. r r r r r r gle 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 b c c. d. r r the " " product cross (28 – 4) The vector components of vector are given by the equations: , ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ , , x y z z y x y z x y z x y z c a b a b a a i a j a k b b i b j b k c c i c j c k c =- = + + = + + = + + c = a×b The Vector Product in terms of Vector Components r r r r r r r $ $ Those familiar with the use of determinants can use the expres , The order of the two vectors in the cross product is impor si c c t nt on a x y z x y...
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This note was uploaded on 06/17/2010 for the course PHYSICS 1322 taught by Professor Michaelgorman during the Summer '10 term at University of Houston.

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28 - (28 – 1) Chapter 28 Magnetic Fields In this chapter...

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