Chapter 17: Electric Forces and Fields
Proton charge
+e +1.6 x 10^-19 C
charging up a neutral body
- anuetral body has equal number os protons and electrons -excess electrons = negative -excess protons = positive
Conductors
-a material is called a conductor is some electrons in it can move around easily -these electrons are called conduction electrons or free electrons -conductors are usually metals and they can carry electric charge from one place to another -the electrons leave behind protons that are bound in atoms, and so are not mobile -a piece of metal can also accept extra electrons or release some of its conduction electrons so the entire object can acquire a net pos or neg charge
Insulators
-a material is called an insulator if no electron in it can move around easily (all electrons are localized) insulators cannot carry electric charge from one place to another -if extra electrons are placed on an insulator, they tend to stay where they were put
electric field lines of point charges
-a positive charge produces an electric field radiating outward, away from the charge -a negative charge produces an electric field directed inward, toward the charge -field lines indicate the direction of the field; the field points in the direction tangent to the field line at any point -the denser the field lines, the stronger the field -for isolated charges, field lines start or end at infinity
for a metal in equilibrium
-any excess electrons must be at the surface -electric field is zero inside a metal in equilibrium (otherwise electrons would move around until it was!)
electric forces and coulomb's law
-assume two charges particles can be modeled as point particles -magnitude of the electric force between the two particles is given by coulomb's law
Electrical charge
-charge is a fundamental property of particles -SI unit of charge is the Coulomb (charles de Coulomb) -symbols are q or Q -electric charge is carried by electrons and protons -in atoms, the number of electrons equals the number of protons, they are electrically neutral
charging by induction
-charging by induction makes use of polarization -the negatively charged rod is first brought near the metal, polarizing the metal -a connection is made from the piece of metal to electrical ground using a wire -some of the electrons will move off the piece of metal and into the electrical ground region -the final step is to remove the grounding wire -the piece of metal will be left w/a net pos charge
Electron charge
-e -1.6 x 10^-19 C
electric field lines of multiple charges
-electric field lines are a graphical way to show the direction and strength of any field at all points in space (draw a series of lines to indicate the direction, so that the field points in the direction tangent to the lines at any point) -the denser the field lines, the stronger the field -electric field lines start on positive and end on negative charges (or at infinity) -the number of lines is proportional to the charge in each case -two field lines never cross (because superposition principle produces a single-valued force)
electric field
-electric force is transmitted through an electric field -an electric field extends from a charge and permeates all of space -the electric field is the force per unit charge -consider a small positive test charge q in an electric field produced by a charge Q -if q is negative, the force is opposite in direction to the field
excess charge on a metal
-electrons move easily through a metal -excess electrons will be distributed evenly on the surface of the metal (since they repel each other and can move)
Gauss's Law
-gauss's law asserts that the electric flux through a closed surface is proportional to the charge enclosed by that surface. -the trick to applying gauss's law is to find a closed surface such that the electric field is constant and the angle to the electric field is constant *Coulomb's law is a special case of Gauss's law
excess charge on an insulator
-if a few electrons are places on (or taken away from) the insulator, they will tend to stay where they are placed (because they can't move freely) -the net charge on the insulator will eventually be neutralized (the excess of electrons will attract free ions from the air, and neutralize the excess charge)
superposition of forces
-if there are more than two charges, the superposition principle must be used -the force b/w any pair of particles is independent of any other charges that may be present -find the forces on the charge of interest due to all the other forces, then add the forces as vectors -draw vectors as if unknown charges are positive
forces between charges
-like charges (both pos or neg) repel each other -unlike charges (pos and neg) attract each other -action reaction principle tells us that the forces on the two particles are equal and opposite
charging an object by rubbing
-the act of rubbing causes some charge to be transferred from one material to another ex: when rubbing amber with fur, electrons are moved from the fur to the amber -the amber acquires a net negative charge, the fur is left with a net positive charge
electric field line density - point charge
-the electric field strength from a point charge is 1/r^2 -the area of a sphere around the charge grows as r^2 *the number of field lines per unit area of the sphere is proportional to the electric field strength
example of electric flux
-the net flux through a box is zero because all of the field lines that go in the left side (θ=180°) come out of the right side (θ=0°)
polarized
-the rod and paper are both initially neutral -the rod is rubbed with fur and obtains a negative charge -the presence of the rod causes the electrons in the paper to be repelled and the positive ions are attracted -the paper is said to be polarized -now, the pos ions in the paper are closer to the neg charges on the rod, so the force attracting the pos ions to the rod is stronger than the force repelling the electrons in the paper from the rod
examples of electric field lines
-two equal charges of opposite sign -two equal positive charges -charges of unequal value and like and unlike sign
Electric flux
-we define the electric flux through a surface where E is the magnitude of the electric field, A is the area of the surface, and θ is the angle between the electric field and the normal to the surface -if the electric field is normal to the surface, the flux is EA. -if it is parallel to the surface, the flux is zero -for a closed surface, the normal points outward
problem solving strategy
1. recognize the principle -electric force can be found using coulomb's law, principle of superposition may be needed 2. sketch the problem -construct a drawing with call charges shown, include a coordinate system, show directions of all forces on the particle 3. calculate the magnitude of the force on the charge in question from each of the other charges 4. determine the direction of each force based on the signs of charges 5. draw a vector diagram including every force on the charge in question 6. determine the vector sum of all of the forces
two equal positive charges
all field lines end at infinity
two equal unlike sign charges:
all field lines end on the negative charge
where do free ions in the air come from
atoms in the air are ionized by radiation
problem solving: electric field from multiple point charges
electric fields obey the superposition principle: the total electric field generated by multiple charges is the vector sum of the field generated by each charge -calculate the magnitude of the field from each of the charges (ignoring the signs) -determine the direction of each field based on the sign of each charge -draw a vector diagram and determine the vector sum of all the fields
basic properties of charges
net charge is conserved in an isolated system -the total charge on an object is the sum of all the individual charges carried by the object -charge can move from place to place, object to object, but net charge of the universe is fixed -charge can be created when particles are created out of energy -NET amount of electrical charge produced in any such process is always zero
