Download PHY481: Electrostatics Semester plans Introductory E&M review (1) Lecture 1

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
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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
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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
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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
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