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 θ with respect to field:
Force per unit length between two long parallel wires carrying currents I, I' separated by a distance r:
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 induction, Lenz's Law, Faraday's Law
Equations:
Induced emf in N coils of wire with changing flux Φ:
Lenz's Law states that the induced emf creates a current that produces a magnetic field to counteract the change in 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 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 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 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:
Inductive reactance : XL = ω L, the current is 90 degrees behind the voltage
(ω = 2π f)
Capacitor reactance: XC = 1/(ωL),
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 ω2 = 1/(LC).
Units:
Magnetic Flux: 1 Weber = 1 Tesla m2
Inductance: 1 Henry = 1 Ω s
Displacement current, the wave nature of light, the Poynting vector.
Equations:
If a changing electric flux ΦE 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,
Frequency f, wavelength λ, 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
Huygen's principle, Single slit diffraction, interference in thin films, polarization, Brewster's angle. The rest of the chapter was covered in the first semester of the course, and will not appear on the exam.
Equations:
The dark bands in single slit diffraction appear at angles θ such that if the width of the slit is D and the wavelength of light is λ, then for any integer m,
Interference in a thin film gives bands for light of wavelength λ 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. The intensity of polarized transmitted through a polarizer rotated at an angle of θ with respect to the polarization axis is
Brewster's angle: Light reflected from an object with index of refraction n is completely polarized in a direction parallel to the object and perpendicular to the direction of the light's travel if the angle of incidence θ satisfies
| Physics 222 | Department of Physics | University of Tennessee |