PY212 SUMMER 2003

Prof. Milos Steinhart

Study Guide for the Final Exam

Friday August 15, 2003 1110-1310

bring a pencil/pen and B.U. ID

Presented bellow is a detailed (though not exhaustive) list of what you are expected to know for each of the major topics to be covered on the exam.

Please note that the exams will test BOTH your understanding of the basic physical concepts AND your problem-solving skills. It will not test memorization; a formula sheet will be appended to the exam. A draft of the formula sheet is appended to this study guide.

You will be expected to know the definitions of relevant concepts, to give concise descriptions of physical laws, to derive relevant equations, and to discuss the various physical models presented in the lectures. You are also expected to master the problem-solving techniques in the discussion sections and the homework.

The exam will consist of 4 problems (each worth 20% of the total) and a set of multiple-choice questions (also worth 20% of the total). To receive a full credit, you must show all of your work. Try to be as clear as possible. Bear in mind that the instructor can see your ideas only through the material, which is written.

Calculators can be used during this exam.

Mathematical Concepts

Be able to …

Divide vector into components in orthogonal axes system, add and subtract vectors, calculate and understand the scalar and vector product of two vectors.

Use the basic goniometric functions: sin, cos, tan, cot

Calculate derivatives and integrals of simple functions of one variable.

Solve sets of linear equations, solve quadratic equations.

Plot graphs of simple functions and indicate slopes, intercepts and areas.

Electrostatics

Be able to …

Understand the concept of the charge and its main properties.

Understand the main properties of forces between point charges.

Understand and use the Coulomb’s law.

Understand the superposition principle.

Understand the concept of the electric field, intensity and its flux.

Understand and use the Gauss’ law.

Understand the concept of a conservative field.

Understand the concept of the potential and potential energy.

Understand the relations between the field potential and intensity at least in fields of special symmetry; uniform and spherically symmetric fields.

Understand the concept of the electric dipole, the field it generates and its behavior in external fields (at least uniform field).

Understand the concept of the capacitance.

Calculate the capacitance for capacitors with simple geometry.

Replace a network of capacitors by a single capacitance. Find individual voltages and charges.

Understand the concepts of potential energy and energy density in electrostatic field.

Electro-kinetics

Be able to …

Understand the concept of the electric current.

Understand the concept of the resistance.

Understand and use the Ohm’s law.

Understand the concept of the electric circuit and its topology.

Understand and use the Kirchhoff’s laws.

Understand the concept of transport of power transport through the electric circuit.

Construct a simple voltmeter or ammeter using a galvanometer.

Magnetism

Be able to …

Understand the concept of the magnetic field and induction.

Calculate the magnetic field produced by straight wires, wire loops, solenoids and toroids with currents.

Apply the Lorenz force formula.

Understand and calculate forces on wires with currents in magnetic field.

Understand the behavior of moving particles in electric and magnetic fields.

Understand the behavior of magnetic dipoles in magnetic field.

Understand the three main types of magnetic behavior of materials: diamagnetic, paramagnetic and ferromagnetic.

Electromagnetism

Be able to …

Understand the Faraday’s law and be able to apply it, at least in simple situations.

Understand the Lenz law and be able to apply it.

Understand the concept of self and mutual inductances.

Understand the counter EMF, counter torque and eddy currents.

Understand how a transformer works.

Understand the behavior of RC, RL and LC circuits after application of an external voltage.

AC Circuits

Be able to …

Understand the concept of the impedance, a phasor, generalized Ohm’s law and their use in simple cases.

Understand the concept of resonance.

Waves

Be able to …

Understand what a wave generally is, what are its parameters and their relations.

Understand the concept of the electromagnetic wave and know quantitative properties of its components including their mutual directions.

Understand how wave changes when propagating in materials.

Optics

Be able to …

Understand the concepts and limits of geometrical optics.

Understand the Fermat’s principle, the concept of a ray, reflection, refraction, optical mirror, a thin lens, focal length and focal plane. Understand the effect of dispersion.

Understand the main concepts of wave optics, Huygens’ principle, coherence, interference and diffraction.
PY212 SUMMER2 2003 Final Exam Formula Sheet

Electron’s charge and mass: e = -1.6 10^-19 C; m_e = 9.1 10^-31 kg

Permeability of vacuum: m₀ = 4p10^-7 Tm/A; Speed of light c = 3 10⁸ m/s

Coulomb’s law (force acting on Q₂) :

;

Electric intensity: The flux of electric intensity:

The Gauss’ law:

Potential and potential energy: DU = Q Dj

The relations of the electric intensity and potential:

Intensity and potential of electric field created by a point charge :

The definition of the capacitance:

Capacitors in series: Q = Q₁ = Q₂; V = V₁ + V₂; 1/C_S = 1/C₁ + 1/C₂

Capacitors in parallel: Q = Q₁ + Q₂; V = V₁ = V₂; C_P = C₁ + C₂

The capacitance of the parallel plate capacitor with dielectric:

The energy of the charged capacitor: Energy density of electric field:

The electric current: The electric current density:

The Ohm’s law: Resistivity and conductivity:

Thermal behavior of resistivity: The electric power:

Kirchhoff’s laws:

Resistors in series and in parallel:

Biot-Savart law: Ampère’s law:

Magnetic force on an infinitesimal (dl) and finite (straight l) length of wire with current I:

Lorentz force on moving charged particle in electric and magnetic fields:

Magnetic dipole moment: Torque on magnetic dipole:

The magnetic flux: Faraday’s law:

The self-inductance of a coil with N loops: … of a solenoid N, A, l, m_r:

Transformer:

Magnetic energy in inductor: The magnetic field energy density:

Time constant RC: Time constant RL: Thompson’s formula:

Impedances: Z_R = R; Z_L = jwL; Z_C = 1/jwC; General. Ohm’s Law: U = ZI

Planar polarized wave: E(x,t) = E₀sin(wt-kx); B(x,t) = B₀sin(wt-kx)

w = 2p/T = 2pf; k = 2p/l; c = fl;

Poynting vector: ; Relative field amplitudes in EMW: B = E/c

Reflection: j₁ = j₂; Refraction - Snell’s law: n₁sinj₁ = n₂sinj₂

Lensmaker’s equation:

Thin lens or mirror equation: 1/d_o + 1/d_i = 1/f