Exam 2 Laundry List PH 316 Fall 2000 (from previous list)

• Give the definition of curl in terms of circulation and area
• State Stokes' theorem, having to do with circulation and curl
• Give the definition of divergence in terms of flux and volume
• State Gauss' theorem, having to do with flux and divergence
• Be able to expand a function in terms of a binomial series, or a taylor series.

• start with flux of J over a closed surface and carefully obtain the continuity equation
• interpret flux of J in terms of what's inside, using conservation of charge
• use divergence theorem
• arrive at div J + d/dt rho = 0
• image charges for planes and spheres
• force of attraction of charge and grounded conducting plane
• force of attraction between grounded conducting sphere and a charge outside the sphere
• force of attraction between charge and hemispherical bump on infinite grounded conducting plane

• make an argument for div B = 0 based on properties of field lines, and divergence theorem
• use div B = 0 to show the normal component of B must be continuous at the boundary between adjacent materials

• electric dipoles
• definition p = qd
• torque on dipole p in external E field
• potential energy U of dipole in external E field
• force on dipole in external E field ( F = - grad U)
• magnetic dipoles
• definition m = I a
• torque on dipole m in external B field
• potential energy of dipole m in external B field
• force on dipole m in external B field ( F = - grad U)
• P = polarization = dipole moment per unit volume
• bound polarization volume charge density
• bound polarization surface charge density
• Given a fairly simple situation (probably a linear dielectric), calculate
• D
• E
• P
• bound charge

• dipoles and images; image charges for charge near a dielectric surface
• linear dielectrics, capacitors filled with dielectric in various ways
• use div D = rho(free) to show that the normal component of D is continuous at the boundary between adjacent materials, unless there is a sheet of free charge present at the boundary

• Biot-Savart law
• calculate B at center of circular loop
• calculate B on axis of circular loop, a distance z from center
• B = curl A
• curl B = mu_o Jfree
• use curl B = Jfree to show ampere's law
• need stokes theorem, interpret area integral of Jfree
• ampere's law: circulation of B around curve C = mu_o I(enclosed by C)
• long straight wire
• inside a solenoid
• near an infinite sheet of current
• use curl H = Jfree to show that parallel component of H is continuous at a boundary between different materials where there is no sheet current density K
• Faraday's law emf = - d/dt (flux of B)
• derive curl E = -dB/dt from faraday's law
• induced current in loop being pulled through a magnetic field
• induced current in a loop surrounding another loop whose flux is changing