# PHYS 142 - Ch.18, Electric Forces and Electric Fields

The physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types: positive (proton) and negative (electron). Like charges repel and unlike attract.
-Losing electrons leads to a + charge, gaining electrons leads to a – charge
Electric Charge
The SI unit for the measuring of the magnitude of an electric charge
e=1.60*10⁻¹⁹ C
-A C is an incredibly powerful charge, such as in a lightning bolt. The charge typically created in the laboratory is a microcoulomb (µC)
Coulomb (C)
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The symbol that represents the magnitude of the charge on a proton or an electron and does not include the algebraic sign that indicated whether the charge is positive or negative.
=1.60*10⁻¹⁹
e
An atom, or any object, carries no net charge, the number of protons and electrons are equal.
Electrically Neutral
A material that readily conducts electrical charge.
– The electrons freely flow due to their place in the valence of the atom
-At equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor.
-At equilibrium under electrostatic conditions, the electric field is zero at any point within a conducting material.
-The conductor shields any charge within it from electric fields created outside the conductor. The shielding results from the induced charges on the conductor surface.
-The electric field just outside the surface of a conductor is perpendicular to the surface at equilibrium under electrostatic conditions.
Electrical Conductor
A material that conducts electricity poorly.
– There are very few electrons free to move throughout the material. Virtually every electron remains bound to its parent atom.
Electrical Insulator
The process of giving one object a net electrical charge by touching it to another object that is already charged.
Charging By Contact
The process of giving one object a net electric charge without touching the object to a second charged object.
-This is done by bringing a charged object near a conductor, attaching a grounding wire to the conductor to release repelled charged, removing the ground wire, and then removing the charged object, leaving the conductor with an unequal number of protons and electrons.
Charging By Induction
The law stating that the magnitude F of the electrostatic force exerted by one point charge q₁ on another point q₂ is directly proportional to the magnitudes |q₁| and |q₂| of the charges and inversely proportional to the square of the distance r between them:
F=k(|q₁||q₂|)/r²
-This gives only the magnitude of the electrostatic force that each point charge exerts on the other; it does not give the direction.
-The electrostatic force is directed along the line joining the charges, and it is attractive if the charges have unlike signs and repulsive if the charges have like signs.
-Similar to Newton’s law of gravitation (F=Gm₁m₂/r²) with one exception: gravity always attracts, EF can attract or repel.
-The EF can be the centripetal force (Fc) of an orbiting electron
Coulomb’s Law
The term ε₀, used in an equation to express Coulomb’s constant, k:
k=1/(4πε₀)
Permittivity of Free Space (ε₀)
Kilogram (kg)
SI Unit for Mass
Meter (m)
SI Unit for Distance
A negligibly small charge that’s put into an electric field to measure it by observing its reaction due to the influence of the electric field.
Test Charge (q₀)
A region around a charged particle or object within which an electrostatic force would be exerted on other charged particles or objects.
E=F/q₀
-This is a vector, and its direction is the same as the direction of the force on a positive test charge.
– It is the surrounding forces that create this at a given point. Any positive or negative charge placed at the point interacts with the field and, as a result, experiences a force.
Electric Field (E)
An electric charge regarded as concentrated in a mathematical point, without spatial extent. The electric field experienced by this at a given distance r from this can be expressed as:
E=k|q|/r² (Note that the q₀ has no effect on this.)
-|q| denotes the magnitude of q, without regard to whether q is + or -. If +q: E is directed away from q, if -q: E is directed towards q.
Point Charge (q)
A device consisting of two parallel metal plates, each with an area A. A charge +q is spread uniformly over one plate, while a charge-q is spread uniformly over the other plate. In the region between the plates and away from the edges, the electric field points from the positive plate toward the negative plate and it’s perpendicular to both. It has a magnitude of:
E=q/ε₀A = σ/ε₀
-Except in the region near the edge, E has the same value for all places between the plates. The field does not depend on the distance from the charges, in distinct contrast to the E created by an isolated point charge.
Parallel Plate Capacitor
The charge per unit area
Charge Density (σ)
A kind of ‘map’ that gives the direction and strength of the field at various places.
-The lines are always directed away from + charges and towards – charges
– The number of lines is proportional to the magnitude of the charge
-These lines always begin on a positive charge and end on a negative charge and do not start or stop in mid-space. Further, the number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.
-The electric field lines are curved around the vicinity of two identical charges. There is an absence of lines in the region between the charges, indicating that the electric field is relatively weak between the charges.
– aka: Lines of Force
Electric Field Lines
This consists of two separated point charges that have the same magnitude but opposite signs. The electric field for this is proportional to the dipole moment.
-For a curved field line, the electric field vector at a point is tangent to the line at that point.
-The pattern of the lines for the dipole indicated that the electric field is greatest in the region between and immediately surrounding the two charges, since the lines are closer together there.
Electric Dipole
The product of magnitude of one of the charges in an electric dipole and the distance between the charges.
Dipole Moment
A situation in which an electric field is produced by charges that are spread out over a region, rather than by a single point charge. This creates an extended collection of charges.
Charge Distribution
The law that describes the relationship between a charge distribution and the electric field it produces. The total flux through a closed surface is equal to the charge inside divided by a constant ε₀.
-This is used to figure out the electric field charge distribution of highly symmetrical shapes.
Gauss’ Law
The measure of flow of the electric field through a given area (the measure of Gauss’ Law). It is proportional to the number of electric field lines going through a normally perpendicular surface.
ΦE = ∑Ei*cosθ*∆Ai (where θ=angle between E and and the normal to the surface.)
ΦE = E/A
ΦE = q/ε₀ (If e is ⊥ to the plane)
Unit: N*m²/C²
Electric Flux (ΦE)
A closed surface in 3-D space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field.
Gaussian Surface

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