Download Phy 203: General Physics III

Phy 203: General Physics III
Ch 18: Electric Forces & Electric Fields
Lecture Notes
Electric Charge
• A fundamental property of protons & electrons
• The SI unit of charge is the coulomb (C)
• Two types of charge (q):
– Positive (+): e.g. protons (qproton = +1.602x10-19 C)
– Negative (-): e.g. electrons (qelectron = -1.602x10-19 C)
• Atoms & molecules have no net charge
– Equal # of protons & electrons
– protons & electrons have the same magnitude but opposite charge
• Properties of charge:
– Like charges repel each other
– Unlike charges attract each other
• Electric charge is quantized
– The smallest unit of charge (e) is 1.602x10-19 C
– The net charge of any matter is
qnet = Ne
• Electric charge is conserved
– There is no known process that can change the charge of something
Coulomb’s Law
• The attractive/repulsive force between charges is called
electric force (remember forces are vectors!)
• The magnitude of the electric force between 2 charges
can be determined by Coulomb’s Law:
q1q2
FE  k 2
r
where:
k is 8.99 x 109 N.m2/C2{Coulomb’s constant}
r is the separation distance between charges
q1 & q2 are the magnitude of charges respectively
• The direction of FE is determined by the sign of the
charges
Charles Augustin de Coulomb
(1736-1806)
• Engineer by education
• Won prize for his work on the
subject of friction
• Won prize for using calculus of
variations to solve engineering
problems
• Published 7 important papers on
electricity & magnetism (between
1785-1791), including:
–
–
–
–
The law of attraction and repulsion
The electric point charges
Magnetic poles
The distribution of electricity on the surface of charged bodies
The Electric Field
• The ability of a charge to influence other charges in its
vicinity its electric field
• The SI units for electric field are N/C
• The electric field is a vector property
– E fields due to multiple charges add as vectors
– E field lines originate at + charges & terminate at - charges
• The direction of an electric field vector (at a point in
space) is the direction of electric force that would be
exerted by on a positive charge at that location
+
-
The Electric Field (cont.)
• The magnitude of electric field for a point charge (q):
q
Ek 2
r
• The force (FE) acting on a “test” charge (qo) placed in
an electric field (E) is
FE = qoE
• Note the similarity of the electric force law to
Newton’s 2nd Law (F=ma)
• Formal definition of electric field:
– the electric force per unit charge that acts on a test charge at
a point in space or
E = FE/qo
Parallel Plate Capacitor
• A parallel plate capacitor consists of 2 conducting plates
separated by a small space (which may be filled with air or some other
dielectric material)
A
+
-
+
-
+
-
+
E
A is surface area
A q is charge on each face
-
E is electric field
+q
-q
• Excess charge (-q) on one inner face repels equal charge away
from the opposite face leaving (+q)
– Charge on each face is uniformly spread out on the surface
• Electric field is constant between the plates
– Electric field lines point from +q to -q
• The electric field (magnitude) inside a parallel plate capacitor is
E = q/eoA = s/eo (for air filled capacitor)
where eo is 8.85 x 10-12 C2/(N.m2), the permittivity constant (free
space) and s is the surface charge density (q/A)
Conductors & Insulators
• Conductors are materials that allow electric charge to
flow (or move through it)
– Excess charge will repel itself pushing all excess charge to the
surface of the conductor
– Under equilibrium conditions, all excess charge resides along
the surface of the conductor
– When electric charge flows along a conductor (i.e. electricity) it
flows along the surface (think about the implications!)
– Electric field inside a conductor is zero
• Insulators are materials that do not allow electric charge
to flow
– Excess charge will remain fixed (or static)
– Excess charge can be inside an insulator or along its surface and
does not have to be uniformly distributed
– Electric charge inside insulator depends on orientation and
quantity of excess charge
Electric Shielding
• As stated previously, the electric field inside
a conducting material is zero (Einside=0)
• If a conductor completely surrounds an
empty space, the electric field inside the
empty space is also zero
– The conductor “shields” any charge inside
region from electric fields produced outside the
conductor
Gauss’ Law
• Gauss’ Law is a fundamental law of nature relating
electric charge to electric flux
• Consider a electric field passing through a region in
space. Electric flux is the product of electric field
normal to the area (E .cosf) and surface area (A) or
FE= (E .cosf).A {electric flux}
Gauss’ Law:
• The total electric flux through any closed (“Gaussian”)
surface is equal to the enclosed charge (Qenclosed)
divided by the permittivity of free space (eo)
FE= S (E .cosf).A = Qenclosed/ eo
• Gauss’ Law can be used to determine the electric field
(E) for many physical orientations (distributions) of
charge
Johann Carl Friedrich Gauss
(1777-1855)
• One of the greatest mathematicians
in history
• Published major works in the fields
of:
– Non-euclidian & differential geometry
– Statistics (including least squares method)
– Potential Theory (hence the term “potential” energy & electric
potential)
– Terrestrial magnetism (including least squares method)
• Made a fortune investing in bonds (is it just me or does
Gauss look strikingly similar to Ebenezer Scrooge??)