HR28 - Chapter 28 Magnetic Fields In this chapter we will...

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(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 G B F G μ G
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One can generate a magnetic field using one of the following methods: Pass a current through a coil and thus form what is known as an "electromagnet". Use a "permane What produces a magnetic field a. b. nt" magnet 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 B B F magnetic field G G field vector . B G (28 – 2)
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North South The iron bar is now weakly magnetized as you can verify by bringing close a magnetic compass. The bar end that faces north is called the north pole of the magnet. The bar end that faces south is known as the south pole of the magnet. Illustration from Gilbert’s book “de Magnete” Recipe for making a weak permanent magnet -Heat up an iron bar so that it looks red-hot and beat it with a hammer. -Align the iron bar while it is still hot along the north-south direction. -Let the iron bar cool in that position
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William Gilbert 1544-1603
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The magnetic field vector is defined in terms of the force it exerts on a charge which moves with velocity . We inject the charge at random directions in a region where we B F qv q Definition of B G G G wish to determine , 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 B B B Fq BF G G GG not zero and its magnitude where is the angle between and . In addition is perpendicular to the plane defined by and . The magnetic force vector is gi s ven by the equatio i n: n B B B v vB F φ = G G G G 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 B B v q Bv v B FB = = SI unit of B : G G G B v B = × G G G sin B v B = (28 – 3)
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Nicola Tesla 1856-1943
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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 ca b a b c c b c φ × = = The Vector Product of two Vectors GG G G G G 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 ab c a right hand rule a.
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HR28 - Chapter 28 Magnetic Fields In this chapter we will...

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