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HR28_post

# HR28_post - Register your iclicker The following 2...

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Register your iclicker • The following 2 iclickers are not registered yet AADF255, FF1CD33 • Check if the one is yours and register asap 1 • Students with these iclicker IDs have resigned? 103298BA, A27DFF2

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Cover the following topics: • Magnetic field vector B • Magnetic force on a moving charge • Magnetic field lines • Motion of a charge particle in an uniform Chapter 28 Magnetic Fields 2 magnetic field • Magnetic force on a current carrying wire • Magnetic torque on a wire loop • Magnetic dipole , magnetic dipole moment t • Hall effect • Cyclotron and Synchrotron particle accelerators
An electric field E is produced by an electric charge In contrast, magnetic field B is not produced by “magnetic charge”. In fact, there is no such thing as “magnetic charge” (often called “magnetic monopole” ) Then how magnetic fields can be created? One way to produce a magnetic field is to use moving electrically charged particles. E.g. current in a wire of an electromagnet Producing Magnetic Field 3 The other way to produce magnetic field is by means of elementary particles such as electrons because these particles have intrinsic magnetic field around them – magnetic field is a basic characteristic of each particle (like mass, charge, etc.) Magnetic fields of electrons in certain materials add together to give a net magnetic field. Permanent magnets are made of this type of materials. In most of other materials magnetic fields of electrons cancel out, producing no net magnetic field

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The magnetic field vector B is defined in terms of the force F it exerts on a charge q which moves with velocity v : – We inject the charge q in a region where we wish to determine B at random directions, trying to scan all possible directions. There is one direction for which the force F B on q is equal to zero. This direction is that of B . For all other directions F B is not zero and its magnitude is B r The Definition of 4 φ |q|vB F B sin = B v q F B r r r × = where φ is angle between the directions of v and B – Furthermore, the direction of F B is always perpendicular to v We can summarize these results with the following vector equation:
The Cross/Vector Product of Two Vectors c = a × b We combine a and b to form a new vector c 1. Magnitude of c : c = absin θ 2. Direction of c : c is perpendicular to the plane defined by a and b , and the direction is given by the right hand rule: when fingers 5 θ sweep a into b , the thumb of the right hand points in the direction of c b a a b v r r r × - = ×

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Vector Product by Components The vector product of two vectors can be calculated using their components , ˆ ˆ ˆ k a j a i a a z y x + + = r , ˆ ˆ ˆ k b j b i b b z y x + + = r b a k c j c i c c z y x r r r × = + + = ˆ ˆ ˆ where: z O x y i j k ^ ^ ^ 6 x y y x z z x x z y y z z y x b a b a c b a b a c b a b a c - = - = - = , , These expressions can be summarized succinctly in the determinant form: z y x z y x b b b a a a k j i c ˆ ˆ ˆ = r
j ˆ i ˆ k ˆ × =

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