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Download PHY481: Electrostatics Semester plans Introductory E&M review (1) Lecture 1
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PHY481: Electrostatics Semester plans Introductory E&M review (1) Lecture 1 Carl Bromberg - Prof. of Physics Preparation from Intro Physics-II Nonexistent – Asleep through most classes, units a mystery, can “p & c” – Passed but still waiting for inspiration Very shaky – Followed lectures, needed help with most homework problems – Exams: familiar problems OK, but often missed the point – Forgot nearly everything, starting close to zero Good but not great – Could do most homework problems without help – Exams: OK going in and out, but didn’t do as well as expected – Needs a refresher, and to fill in the gaps Confident – Concepts strong, did extra problems, ready for tough stuff. Lecture 1 Carl Bromberg - Prof. of Physics 1 Plan of attack Compassionate review – 2 weeks reviewing Intro E&M concepts, including brief descriptions and solving “familiar” problems Followed by the typical course content – 2 weeks developing advanced mathematics and techniques – Full description of each topic in Electrostatics, using advanced mathematics, and solving problems with a large range of difficulty – Exams: ~50% at an Intro E&M level, ~50% with focus on advanced techniques. – I expect that you can, at a minimum, do the Intro problems! Lecture 1 Carl Bromberg - Prof. of Physics 2 Properties of classical electric charge Electric Charge – Property of matter associated with the electromagnetic force – Magnitude quantized in units (or 1/3) of electron charge e e = 1.6 × 10 −19 C – Two signs + (proton) and – (electron), also neutral (neutron) All matter begins as a collection of neutral atoms – Electrons can move from one object to another. – To make an object + (–), remove (add) electrons. – An object with charge +q, implies a net charge –q elsewhere. Charge densities ρ, σ, λ with simple space dependences Lecture 1 Volume Surface Line dq = ρ dV dq = σ dS dq = λ d Carl Bromberg - Prof. of Physics 3 Force between charges Force between two charges, Coulomb’s Law: Force on 1 is in direction of r 1 q1q2 F1 = r̂ 2 4πε 0 r same charge sign Superposition principle Will need new notation later! 2 1 Nm = 9.0 × 109 4πε 0 C2 r r̂ = points from q2 to q1 r q1 and q2 carry charge sign – Force on charge q from charges q1,q2, ... qk is the vector sum of forces between q and each of the charges. – No interference between action of the charges Lecture 1 Carl Bromberg - Prof. of Physics 4 The electric field Charge creates an electric field – A very small positive charge q placed at a point P experiences a force F from a collection of charge Q (seems positive). – The electric field E at the point P is defined as F E= q E P q is gone! Q Electric field lines – begin on + charge and end on – charge – direction of E is along field lines – E field lines do not cross – density of lines is α to field magnitude Lecture 1 positive point charge Carl Bromberg - Prof. of Physics 5 Electric fields from charge distributions Integration over charge distributions 1 E= 4πε 0 dq′ ∫ r ′ 2 r̂′ dq′ = ρ dV ′ Q = ∫ ρ dV ′ E-fields of simple charge distributions & density – Sphere, cylinder, box - volume charge density ρ – Sphere, cylinder, box, sheet - surface charge density σ – Thin line, ring - linear charge density λ – Sheets, rings and lines, which may be of infinite extent Lecture 1 Carl Bromberg - Prof. of Physics 6 Coordinate systems Unit vectors, differential line and space elements dx – Cartesian î, ĵ, k̂ dV = dx dy dz – Cylindrical r̂, φ̂, k̂ – Spherical r̂, θ̂, φ̂ dr (radial) or rdφ (ring) dV = rdrdφ dz dr (radial), rdθ (polar), r sin θ dφ (ring) dV = r 2 dr sin θ dθ dφ – Symmetry used to avoid angular complications – Radial and angular unit vectors needed later. Warm up! From the above, determine the volume and surface area of a cylinder & sphere of radius R. Lecture 1 Carl Bromberg - Prof. of Physics 7