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Lecture 18

# Lecture 18 - (31 20 i I sin t 1 XC C A B Z R2 X L X C tan 2...

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O A B From triangle OAB we have: tan We distinguish the following three cases depending on the relative values of and . 0 The current phasor lags behind the generat L C L C L C R LL LC V V IX IX X X V IR R XX 1. or phasor. The circuit is more inductive than capacitive The current phasor leads ahead of the generator phasor The circuit is more capacitive than inductive The current phaso CL 2. 3. r and the generator phasor are in phase   sin i I t     2 2 Z R X X L XL tan R 1 C X C (31 - 20)

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In an LRC circuit, if X L > X C , the circuit is said to be predominantly “inductive.” This is because: 1 2 3 4 5 0% 0% 0% 0% 0% 1. L (in Henrys) > C (in Farads) 2. L (in Henrys) = C (in Farads) 3. L (in Henrys) < C (in Farads) 4. The circuit behaves more like an RL circuit than an RC circuit 5. The current leads the emf in the circuit
Lecture 18 March 25, 2010 Chapter 32 Maxwell’s equations & Magnetism in matter

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Outline: -Gauss’ law for magnetism - The missing term from Ampere’s law added by Maxwell - The magnetic field of the earth - Orbital and spin magnetic moment of the electron - Diamagnetic materials - Paramagnetic materials - Ferromagnetic materials (32 – 1)
Fig.a Fig.b In electrostatics we saw that positive and negative charges can be separated. This is not the case with magnetic poles, as is shown in the figure. In fig.a we have a p Gauss' Law for the magnetic field ermanent bar magnet with well defined north and south poles. If we attempt to cut the magnet into pieces as is shown in fig.b we do not get isolated north and south poles. Instead new pole faces appear on the newly cut faces of the pieces and the net result is that we end up with three smaller magnets, each of which is a i.e. it has a north and a south pole. This result can be expr magnetic dipole essed as follows: The simplest magnetic structure that can exist is a magnetic dipole. Magnetic monopoles do not exists as far as we know. (32 – 2)

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i B ˆ i n i ΔA i 11 2 Magnetic flux cos Take the limit of the sum as cos Gauss' law for magnetic field: T m known as the "Weber" (Wb) 0 nn i i i i ii B B dA n BdA B dA B dA          SI magnetic flux unit : (32 – 3)
Physical meaning of Gauss' law for the magnetic field Gauss' law for the magnetic field expresses the fact that there is no such a thing as a " ". It also indicates that the magne magnetic charge tic field lines are closed. Note: Gauss' law for the electric field: enc E o q E dA   (32 – 4)

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The statement that magnetic field lines form closed loops is a direct consequence of: 1 2 3 4 5 0% 0% 0% 0% 0% 1. Faraday’s law 2. Ampere’s law 3. Gauss’ law for electricity 4. Gauss’ law for magnetism 5. the Lorentz force
Faraday's law states that: Using symmetry argument, Maxwell extended Ampere's law into: known as " " The el E oo B o enc d E dS dt B S i d dt d     Induced magnetic fields

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Lecture 18 - (31 20 i I sin t 1 XC C A B Z R2 X L X C tan 2...

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