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Some of the material on electric fields and DC circuits may be needed in some problems. This material is very basic to the course, and may appear at any time.
Magnets, magnetic poles, Ampere's Law, Teslas, and insulators, magnetic field lines, right hand rules, ferromagnetism, paramagnetism, diamagnetism, magnetic permeability.
Equations:
Force per unit length of a magnetic field B on a current I at angle q with respect to field:
Force per unit length between two long parallel wires carrying currents I, I' separated by a distance r:
Force of a magnetic field B on a charge q traveling at speed v at an angle of q with respect to the field:
In each case, the direction of the force due to a magnetic field is given by a right-hand rule. These are described in the textbook.
A charged particle with mass m and charge q in a constant magnetic field B perpendicular to its velocity v will move in a circle of radius
Magnetic fields are vectors, and must be added using vector addition. The direction of the field is given by the right hand rule.
Ampere's Law: The average value of the parallel component of the magnetic field around a closed loop of length l surrounding a current I is
Solenoid: The magnetic field inside a solenoid with n turns per unit length is
The MKS unit of magnetic field is the Tesla (T). 1 T = 1 N/(Am).
Magnetic flux, magnetic induction, Lenz's Law, Faraday's Law
Equations:
Magnetic flux is defined to be FM is defined to be the average perpendicular component of the magnetic field passing through a surface, times the area of the surface.
Induced emf in N coils of wire with changing flux FM:
Lenz's Law states that the induced emf creates a current that produces a magnetic field to counteract the change in magnetic flux. The path does not have to be around a wire: the emf is generated about any path, and if it is through a conductor, a current will flow in the direction indicated by Lenz's law. In general, this current is called an eddy current.
EMF in a wire of length l moving perpendular to a magnetic field which is also perpendicular to the wire:
Mutual Inductance: The changing magnetic flux produced by a changing current in one coil will induce an emf in a nearby coil:
Transformers are a pair of coils with the magnetic flux of one to be arranged to go entirely through the other, for maximum mutual inductance. The voltages across the primary and secondary coils are related by Vs / Vp = Ns/Np. If the transformer is 100% efficient, the power going into the primary is the same as the power coming out of the secondary coil.
Self Inductance: The changing magnetic flux produced by a changing current in a coil will induce an emf in itself opposing the change in the current:
Solenoid: The inductance of a solenoid (coil of wire) with N loops, length l, and cross-sectional area A is
Energy density stored in a magnetic field:
Time constant for changing current in an inductor-resistor pair:
Reactance X is a constant of proportionality between the peak (or rms) values of the voltage and current in an AC circuit:
In an AC circuit, the current and voltage are not necessarily in phase. Kirchov's Laws still apply at any time, but they do not apply to the peak values, since the peak values do not occur at the same time. For example, if two out-of-phase currents are added, the total peak current is not the sum of the individual peak currents, but somewhat less.
Inductive reactance : XL = wL, the current is 90 degrees behind the voltage
(w = 2p f)
Capacitor reactance: XC = 1/wL,
the current is 90 degrees ahead of the voltage.
LC Resonance: A capacitor and inductor which are tuned correctly to receive the signal. The condition is that w2 = 1/(LC).
Units:
Magnetic Flux: 1 Weber = 1 Tesla m2
Inductance: 1 Henry = 1 W s
Electric flux, displacement current, the wave nature of light, the Poynting vector.
Equations:
Electric flux FE is defined to be the average perpendicular component of an electric field passing through a surface, times the area of the surface.
If a changing electric flux FE passes through the loop used in Ampere's law, the changing electric flux produces a magnetic field in the loop, equivalent to an additional current called the displacement current,
Speed of electromagnetic waves = c, where
Frequency f, wavelength l, and the speed of the wave c are related by
In an electromagnetic wave, the electric and magnetic fields, and the direction of travel are all perpendicular. The electric and magnetic field strengths are related by
The Poynting Vector gives the amount of power per unit area transmitted by the wave. This may be considered to by the intensity of the wave. It points in the direction of travel of the wave. Its average value is
The average value of the Poynting vector is half its peak value.
Huygen's principle, Single and double slit diffraction, diffraction gratings, dispersion, interference in thin films, polarization.
Equations:
The dark bands in single slit diffraction appear at angles q such that if the width of the slit is D and the wavelength of light is l, then for any integer m,
The bright bands for double slit diffraction or a diffraction grating occur at angles q such that if the separation of the slits is D and the wavelength of light is l, then for any integer m,
Interference in a thin film gives bands for light of wavelength l when the thickness t satisifes
The bands are bright or dark depending on the relative phase shifts upon reflecting from the edges of the film: There is a 180 degree phase shift when reflecting from a material with a greater index of refraction, but none when reflecting from a material with a lesser index of refraction. If the relative reflective phase change from the two edges is zero, the previous equation gives bright fringes, while if it is 180 degrees, the previous equation gives dark fringes, and the bright ones appear half-way between these.
Polarization: A polarizer picks out one component of the electric field vector in the light, which aligns with the polarizing axis. If unpolarized light passes through a polarizer, the intensity is reduced by a factor of 1/2.
The intensity of polarized transmitted through a polarizer rotated at an angle of q with respect to the polarization axis is
| Physics 222 | Department of Physics | University of Tennessee |