PHYS 012A Lecture Notes - Lecture 6: Surface Charge, Resultant Force, Stationary Point
12 Jun 2018
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Chapter 23: Electricity and Magnetism 9/18/17
Electric Charges
- Can be positive (proton) or negative (electron). Same sign charges repel, opposite sign charges
attract.
- A rubber rod is negatively charged, and a glass rod is positively charged. They attract.
o Two rubber rods repel.
- Can charge by friction – rubbing a glass rod with silk to transfer electrons and protons.
Conductors
- Electrical conductors are materials in which some of the electrons are free electrons.
o Free electrons are not bound to the atoms.
o These electrons can move relatively freely through the material.
- Whe harged, a good odutor’s harge distriutes itself oer the hole surfae of the aterial.
Insulators
- Electrical insulators are materials in which all of the electrons are bound to atoms.
o They cannot move freely.
- Whe harged, the good isualtors’s harge is uale to oe to other regios of the aterial.
What happens when a charged insulator is placed near an uncharged metallic object?
- They attract each other.
Semiconductors
- The electrical properties of semiconductors are somewhere between those of insulators and
conductors.
- The electrical properties of semiconductors can be charged by the addition of controlled amounts
of certain atoms to the material.
Charging by Induction
- No contact with the object induces charge.
- A charged rubber rod is placed near the sphere without touching it, electrons in the sphere are
redistributed, the sphere is grounded, and some electrons leave the sphere through the ground
wire. Ground wire is removed, there will be more positive charges, but they are not uniformly
distributed. The positive charge has been induced in the sphere. Rod is removed, electrons on
sphere redistribute themselves. Net positive charge on the sphere. Charge is now uniformly
distributed.
Charge Rearrangement in Insulators
- Charges within the molecules of the material are rearranged.
- The proximity of the positive charges on the surface of the object and the negative charges on the
surface of the insulator results in an attractive force between the object and the insulator.
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Coulo’s La
- The force is inversely proportional to the square of the separation r between the charges and
directed along the line joining them.
- The force is proportional to the product of the charges, q1 and q2, on the two particles.
- The eletrial fore etee to statioary poit harges is gie y Coulo’s La.
- The force is attractive if the charges are of opposite sign and repulsive if of like sign. The force is
conservative.
Ke = 9.0 x 109 N*m2/C2 = 1/(4pi(epsilono))
Epsilono (the permittivity of free space)= 8.85 x 10-12 C2/N*m2
E is the smallest unit of charge except quarks.
- e = 1.6 x 10-19 C
- So 1C needs 6.24 x 1018 electrons or protons
Point Charge
- The term point charge refers to a particle of zero size that carries an electric charge.
o The electrical behavior of electrons and protons is described by point charges.
Vector Nature of Electric Forces
- The like charges produce a repulsive force between them
- F21 = -F12
o With like signs for the charges, the product q1q2 is positive and the force is repulsive.
- Unlike charges produce an attractive force between them.
o With unlike signs for the charges, the product q1q2 is negative and the force is attractive.
Multiple Charges
- The resultant force on any one charge equals the vector sum of the forces exerted by the other
individual charges that are present.
- The resultant force on q1 is the vector sum of all the forces exterted on it by other charges.
Zero Resultant Force, Ex
- Where is the resultant force equal to zero?
o The magnitudes of the individual forces will be equal, and directions will be opposite.
This will result in a quadratic.
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Fields
Scalar Field – value (magnitude) of a scalar at every point in space
Vector Field – value (magnitude and direction) of the vector at every point in space (magnitude and
direction) at every point in space
Source – the point where everything comes out of
Sink – where everything goes into
Gravitational Field of the Earth
Visualizing Vector Fields: Field Lines
- Direction of Field line at any point is tangent to the field at that point
o Density tells you the magnitude of the lines. Where the lines are more spread out, the
force is weaker.
- Field Lines Never cross each other because
- Field line density is proportional to magnitude of the field
Vector Field: Gravitation
- Gravitational Force
- Gravitational Field
Created by M
- F = mg is felt by m
- r in the denominator is a length, r hat is a unit vector of magnitude 1 that points away from the
coordinate system.
- Closer to earth, acceleration due to gravity grows.
o The earth creates a gravitational field everywhere, so it is the center point.
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Document Summary
Can be positive (proton) or negative (electron). Same sign charges repel, opposite sign charges attract. A rubber rod is negatively charged, and a glass rod is positively charged. Can charge by friction rubbing a glass rod with silk to transfer electrons and protons. Electrical conductors are materials in which some of the electrons are free electrons: free electrons are not bound to the atoms, these electrons can move relatively freely through the material. Whe(cid:374) (cid:272)harged, a good (cid:272)o(cid:374)du(cid:272)tor"s (cid:272)harge distri(cid:271)utes itself o(cid:448)er the (cid:449)hole surfa(cid:272)e of the (cid:373)aterial. Electrical insulators are materials in which all of the electrons are bound to atoms: they cannot move freely. Whe(cid:374) (cid:272)harged, the good i(cid:374)sualtors"s (cid:272)harge is u(cid:374)a(cid:271)le to (cid:373)o(cid:448)e to other regio(cid:374)s of the (cid:373)aterial. The electrical properties of semiconductors are somewhere between those of insulators and conductors. The electrical properties of semiconductors can be charged by the addition of controlled amounts of certain atoms to the material.
