33–122 Electomagnetism
Autumn Semester 2017
(a course for chemists and biologists)

Overview

Syllabus

Problem Sets

Grades

Overview and purpose of the course

This course explores electromagnetism and light.  On everyday scales down to atomic and molecular scales, the eletromagnetic force is responsible for most of the properties that we observe in materials and in living organisms.
     We shall begin our study of this force by exploring electric and magnetic phenomena separately and in simple situations where charges are either not moving at all or are only moving steadily.  Once we have explored this corner of the natural world, we shall learn that these two phenomena are related and that they are really just two manifestations of a single electromagnetic force.
     Light is also produced by electromagnetism—light arises as oscillations in the electric and magnetic fields. Light is an important example of a wave phenomenon; waves are important in physics since they occur in many different parts of the natural world. The course will conclude with a discussion of optics.
     From time to time we shall illustrate how electromagnetism and light can be used in specific medical applications.

Schedule:

Week I

28 Aug–1 Sept

Electrostatics; Coulomb’s law; Coulomb’s constant; the charge of an electron; the electric field; the principle of superposition; electric field diagrams; distributions of charges; spherically symmetric distributions; a long, thin line of charge

Week II

5–8 September

The electric potential; volts; electron-volts (a unit of energy); how to calculate the electric potential; the potential of a point charge

Week III

11–18 September

Electric dipoles; the electric dipole moment; the electric field due to a dipole, far from the dipole; dipoles in electric fields; dipoles like to align with electric fields; the potential energy of of dipole; capacitors and capacitance; C=Q/V

Week IV

18–22 September

Farads; a parallel plate capacitor; the energy in a capacitor; dielectrics; effect of a dielectric on a capacitor; the dielectric constant, K; symmetries in nature; symmetries in distributions of charge; examples: rotations, translations, mirror reflections; how to use symmetries to determine the direction of an electric field at a point; how to use symmetries to relate the electric field at different points; example: a line of charge

Week V

25–29 September

The electric flux, Φ; Gauss’s law; examples of Gauss’s law; how to choose a Gaussian surface based on the symmetry; electric fields vanish inside conductors and are perpendicular to the surface in electrostatics; direct currents; the drift velocity; the conductivity, σ; the resistivity, ρ; the resistance; ohms (Ω); Ohm’s law, V=IR

Week VI

2–6 October

The electromotive force; power dissipated in a resistor, P=IV=I2R; Kirchhoff’s rules; ΔV=0 around a closed loop; the current entering a node must equal the current leaving the node; resistors in parallel and in series; RC circuits; discharging a capacitor; charging a capacitor with a battery; the time constant of an RC circuit, t0=RC

Week VII

9–13 October

The anatomy of a nerve cell; myelinated and unmyelinated axons; Schwann cells; nodes of Ranvier; the resistance and capacitance of an axon membrane; the leakage resistance; the resting potential; the Nernst equation; the sodium-potassium pump; the response of an axon to a weak stimulus; the action potential

Week VIII

16–19 October

Magnetic fields; the Lorentz force law; teslas; the magnetic force on a streight wire; the magnetic field on a curved wire; magnetic dipoles; the magnetic dipole moment, μ = IA; calculating the torque on a current loop; the energy of a magnetic dipole in a magnetic field

Week IX

23–27 October

Atomic dipoles; spin; magnets; a velocity selectors; mass spectrometers; the Biot-Savart law; the Biot-Savart constant; the magnetic field for an infinite straight wire; the magnetic field for a current loop

Week X

30 Oct–3 Nov

Ampère’s law; the magnetic field of an infinite wire revisited; a solenoid; the magnetic field inside a solenoid; time-dependent magnetic fields

Week XI

6–10 November

The magnetic flux, Φ; Faraday’s law; Lenz’s law; generators; alternating currents; properties of a sinusoid; angular frequency, amplitude; phase shift; period; freqency; hertz (Hz); the effective or root mean square current; transformers; mutual inductance, M

Week XII

13–17 November

Self-inductance, L; the inductance of a solenoid; the energy in an inductor; magnetic materials; the magnetic constant; diamagentic, paramagnetic, and ferromagnetic materials; nuclear magnetic resonance; the nuclear magneton; relation between the spin and dipole moment of a proton; torque on a proton in a magnetic field; precession

Week XIII

20–21 November

How to measure the precession frequency; resonance; chemical shift

Week XIV

27 Nov–1 December

Maxwell’s equations; general properties and examples of waves; travelling waves; sinusoids again; amplitude; phase shifts; wavelength; wave number; wave speed; period; angular frequency; frequency; combining waves; standing waves; interference between waves; constructive and destructive interference; beats; average and differences of two frequencies; the beat frequency; how waves behave at boundaries; boundary conditions; fixed boundary conditions; free boundary conditions; finding the allowed wave numbers and wavelengths for standing waves with boundaries; fundamentals and harmonics;

Week XV

4–8 December

Energy and momentum in waves; the energy density in an electromagnetic field; transverse waves; polarisation; polarisers; circular polarisation; wave properties of light; the index of refraction, n; the reflectance, R; the transmittance, T; spherical waves and plane waves; reflection of light; specular reflection; refraction of light; Snell’s law; total internal reflection

Additional resources

Help Sessions:   6:30–8:30 pm on Wednesday and Thursday evenings in Doherty A200

The teaching assitants will be available to help you with any questions about the problem sets and the material in the course.