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- Electric Forces and
- Electric Fields
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- Discuss electrostatics and its history.
- State the Law of Conservation of Charge.
- Explain Coulomb’s Law, Gauss’s Law, Principle of Superposition, Electric
Dipoles, Potential Energy of Dipoles, and Electric Flux.
- State some applications of electrostatics to everyday life.
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- An electrostatic generator designed and built by Robert J. Van de Graaff
in 1929
- Charge is transferred to the dome by means of a rotating belt
- Eventually an electrostatic discharge takes place
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- The word electricity comes from the Greek word for amber, elektron.
- So the study of electrostatics began with someone figuring out that when
amber is rubbed it attracts other objects.
- Centuries went by, however, before anyone really figured out what caused
this to happen.
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- Danish physicist and philosopher who, in 1819, discovered the deflection
of a compass needle while performing a demonstration for his students.
This discovery of a fundamental connection between electricity and magnetism.
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- Noticed that when a wire
was moved near a magnet, an electric current is observed in the wire.
Faraday described his numerous experiments in electricity and
electromagnetism in three volumes entitled Experimental Researches in
Electricity (1839, 1844, 1855)
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- Maxwell's formulation of electricity and magnetism was published in A
Treatise on Electricity and Magnetism (1873), which included the
formulas today known as the Maxwell equations.
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- Two types of charges exist
- They are called positive and negative
- Named by Benjamin Franklin
- Like charges repel and unlike charges attract one another
- Nature’s basic carrier of positive charge is the proton
- Protons do not move from one material to another because they are held
firmly in the nucleus
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- Nature’s basic carrier of negative charge is the electron
- Gaining or losing electrons is how an object becomes charged
- Electric charge is always conserved
- Charge is not created, only exchanged
- Objects become charged because negative charge is transferred from one
object to another
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- Charge is quantized
- All charge is a multiple of a fundamental unit of charge, symbolized by
e
- Electrons have a charge of –e
- Protons have a charge of +e
- The SI unit of charge is the Coulomb (C)
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- Conductors are materials in which the electric charges move freely
- Copper, aluminum and silver are good conductors
- When a conductor is charged in a small region, the charge readily
distributes itself over the entire surface of the material
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- Insulators are materials in which electric charges do not move freely
- Glass and rubber are examples of insulators
- When insulators are charged by rubbing, only the rubbed area becomes
charged
- There is no tendency for the charge to move into other regions of the
material
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- The characteristics of semiconductors are between those of insulators
and conductors
- Silicon and germanium are examples of semiconductors
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- A charged object (the rod) is placed in contact with another object (the
sphere)
- Some electrons on the rod can move to the sphere
- When the rod is removed, the sphere is left with a charge
- The object being charged is always left with a charge having the same
sign as the object doing the charging
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- When an object is connected to a conducting wire or pipe buried in the
earth, it is said to be grounded
- A negatively charged rubber rod is brought near an uncharged sphere
- The charges in the sphere are redistributed
- Some of the electrons in the sphere are repelled from the electrons in
the rod
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- The region of the sphere nearest the negatively charged rod has an
excess of positive charge because of the migration of electrons away
from this location
- A grounded conducting wire is connected to the sphere
- Allows some of the electrons to move from the sphere to the ground
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- The wire to ground is removed, the sphere is left with an excess of
induced positive charge
- The positive charge on the sphere is evenly distributed due to the
repulsion between the positive charges
- Charging by induction requires no contact with the object inducing the
charge
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- In most neutral atoms or molecules, the center of positive charge
coincides with the center of negative charge
- In the presence of a charged object, these centers may separate slightly
- This results in more positive charge on one side of the molecule than
on the other side
- This realignment of charge on the surface of an insulator is known as polarization
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- The charged object (on the left) induces charge on the surface of the
insulator
- A charged comb attracts bits of paper due to polarization of the paper
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- Coulomb shows that an electrical force has the following properties:
- It is inversely proportional to the square of the separation between
the two particles and is along the line joining them
- It is proportional to the product of the magnitudes of the charges q1
and q2 on the two particles
- It is attractive if the charges are of opposite signs and repulsive if
the charges have the same signs
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- Mathematically,
- ke is called the Coulomb Constant
- Typical charges can be in the µC range
- Remember, Coulombs must be used in the equation
- Remember that force is a vector quantity
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- Two point charges are separated by a distance r
- The like charges produce a repulsive force between them
- The force on q1 is equal in magnitude and opposite in
direction to the force on q2
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- Two point charges are separated by a distance r
- The unlike charges produce a attractive force between them
- The force on q1 is equal in magnitude and opposite in
direction to the force on q2
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- This is the second example of a field force
- Remember, with a field force, the force is exerted by one object on
another object even though there is no physical contact between them
- There are some important differences between electrical and
gravitational forces
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- Both are inverse square laws
- The mathematical form of both laws is the same
- Electrical forces can be either attractive or repulsive
- Gravitational forces are always attractive
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- The resultant force on any one charge equals the vector sum of the
forces exerted by the other individual charges that are present.
- Remember to add the forces vectorially
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- The force exerted by q1 on q3 is F13
- The force exerted by q2 on q3 is F23
- The total force exerted on q3 is the vector sum of F13
and F23
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- Maxwell developed an approach to discussing fields
- An electric field is said to exist in the region of space around a
charged object
- When another charged object enters this electric field, the field
exerts a force on the second charged object
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- A charged particle, with charge Q, produces an electric field in the
region of space around it
- A small test charge, qo, placed in the field, will experience
a force
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- Mathematically,
- Use this for the magnitude of the field
- The electric field is a vector quantity
- The direction of the field is defined to be the direction of the
electric force that would be exerted on a small positive test charge
placed at that point
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- The electric field produced by a negative charge is directed toward the
charge
- A positive test charge would be attracted to the negative source charge
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- The electric field produced by a positive charge is directed away from
the charge
- A positive test charge would be repelled from the positive source
charge
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- The test charge is required to be a small charge
- It can cause no rearrangement of the charges on the source charge
- The electric field exists whether or not there is a test charge present
- The Superposition Principle can be applied to the electric field if a
group of charges is present
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- Units
- When using ke, charges must be in Coulombs, distances in
meters and force in Newtons
- If values are given in other units, they must be converted
- Applying Coulomb’s Law to point charges
- Use the superposition principle for more than two charges
- Use Coulomb’s Law to find the individual forces
- Directions of forces are found by noting that like charges repel and
unlike charges attract
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- Calculating Electric Fields of point charges
- The Superposition Principle can be applied if more than one charge is
present
- Use the equation to find the electric field due to the individual
charges
- The direction is given by the direction of the force on a positive test
charge
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- A convenient aid for visualizing electric field patterns is to draw
lines pointing in the direction of the field vector at any point
- These are called electric field lines and were introduced by Michael
Faraday
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- The field lines are related to the field by
- The electric field vector, E, is tangent to the electric field lines at
each point
- The number of lines per unit area through a surface perpendicular to
the lines is proportional to the strength of the electric field in a
given region
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- Point charge
- The lines radiate equally in all directions
- For a positive source charge, the lines will radiate outward
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- For a negative source charge, the lines will point inward
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- An electric dipole consists of two equal and opposite charges
- The high density of lines between the charges indicates the strong
electric field in this region
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- Two equal but like point charges
- At a great distance from the charges, the field would be approximately
that of a single charge of 2q
- The bulging out of the field lines between the charges indicates the
repulsion between the charges
- The low field lines between the charges indicates a weak field in this
region
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- Unequal and unlike charges
- Note that two lines leave the +2q charge for each line that terminates
on -q
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- The lines for a group of charges must begin on positive charges and end
on negative charges
- In the case of an excess of charge, some lines will begin or end
infinitely far away
- The number of lines drawn leaving a positive charge or ending on a
negative charge is proportional to the magnitude of the charge
- No two field lines can cross each other
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- When no net motion of charge occurs within a conductor, the conductor is
said to be in electrostatic equilibrium
- An isolated conductor has the following properties:
- The electric field is zero everywhere inside the conducting material
- Any excess charge on an isolated conductor resides entirely on its
surface
- The electric field just outside a charged conductor is perpendicular to
the conductor’s surface
- On an irregularly shaped conductor, the charge accumulates at locations
where the radius of curvature of the surface is smallest (that is, at
sharp points)
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- The electric field is zero everywhere inside the conducting material
- Consider if this were not true
- if there were an electric field inside the conductor, the free charge
there would move and there would be a flow of charge
- If there were a movement of charge, the conductor would not be in
equilibrium
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- Any excess charge on an isolated conductor resides entirely on its
surface
- A direct result of the 1/r2 repulsion between like charges
in Coulomb’s Law
- If some excess of charge could be placed inside the conductor, the
repulsive forces would push them as far apart as possible, causing them
to migrate to the surface
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- The electric field just outside a charged conductor is perpendicular to
the conductor’s surface
- Consider what would happen it this was not true
- The component along the surface would cause the charge to move
- It would not be in equilibrium
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- On an irregularly shaped conductor, the charge accumulates at locations
where the radius of curvature of the surface is smallest (that is, at
sharp points)
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- Any excess charge moves to its surface
- The charges move apart until an equilibrium is achieved
- The amount of charge per unit area is greater at the flat end
- The forces from the charges at the sharp end produce a larger resultant
force away from the surface
- Why a lightning rod works
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- Faraday’s Ice-Pail Experiment
- Concluded a charged object suspended inside a metal container causes a
rearrangement of charge on the container in such a manner that the sign
of the charge on the inside surface of the container is opposite the
sign of the charge on the suspended object
- Millikan Oil-Drop Experiment
- Measured the elementary charge, e
- Found every charge had an integral multiples of e
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- Field lines penetrating an area A perpendicular to the field
- The product of EA is the flux, Φ
- In general:
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- ΦE = E A sin θ
- The perpendicular to the area A is at an angle θ to the field
- When the area is constructed such that a closed surface is formed, use
the convention that flux lines passing into the interior of the volume
are negative and those passing out of the interior of the volume are
positive
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- Gauss’ Law states that the electric flux through any closed surface is
equal to the net charge Q inside the surface divided by εo
- εo is the permittivity of free space and equals 8.85 x
10-12 C2/Nm2
- The area in Φ is an imaginary surface, a Gaussian surface, it does
not have to coincide with the surface of a physical object
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- The calculation of the field outside the shell is identical to that of a
point charge
- The electric field inside the shell is zero
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- Use a cylindrical Gaussian surface
- The flux through the ends is EA, there is no field through the curved
part of the surface
- The total charge is Q = σA
- Note, the field is uniform
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