Entire Physics 7D Lecture/Textbook Notes.doc

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Herbert J.Hopster

Physics 7D 1 21 Electric Charge and Electric Field • Electrostatics o interactions between electric charges that are at rest • sign of charge related to attraction o two positively charge objects will repel  same with negatively o a negative and a positive charge will always attract • principle of electric charge o in a closed system, the sum of all electric chrages is constant • an electron has the same charge magnitude as a proton o must be a whole number (can't have a fraction of a charge) • transferring charges o conductor  transfers charge  has free electrons that are willing to travel o insulator  does not transfer charge  doesn't have many, or any, free electrons  complicated molecules  only a handful of elements (carbon, sulfur, phosphorus) are insulators • rubbing 2 insulators together can result in one having a - charge while the other has a + o doesn't work for conductors • induction o charging a body with the opposite sign of an object without losing the charge of the object o induced charge - areas of, say a ball, whose sides both have excess opposite charges o • charged objects can attract an insulator Physics 7D 2 o • Coulomb o the SI unit of electric charge o represents the magnitude of the charge of about 6*10^18 electrons  an electron has a charge of 1.602*10^-19 • Coulomb's law o  electric force between two point charges (N) = (constant)(|charge of one object * charge of the other object|)/(distance between them ^2)  absolute values because the force can not be -, but the charges can  constant usually = 9*10^9 (N m^2)/C^2  for 1 C charges. if 2 C, then multiply by 2  because epsilon-nought usually = 8.854*10^-12 C^2/(N m^2) o principle of superposition of forces  Coulomb's law holds true for an infinite number of point charges  ex. when two charges exert forces simultaneously on a third, the total force on that charge is the vector sum of the forces the two would exert individually • force o equal and oppsoite (F[a on b] is - F[b on a]) o  • electric field o a body with a charge exerts an electric field whether another charge is there to feel it or not o o E is around A, test charge qo feels the force:  Physics 7D 3  F = ma = (charge)(electric field) o o finding E    Electric Field Vector = (coonstant)(point charge)(unit vector between source point and field point; S and P)/(distance between the two)  o Vector field  the varying from point to point of the electric field of a point charge  for large objects, calculating the net electric force of point charges (infinite) on the body is the only way to accurately calculate the actual force  Physics 7D 4 o o • Superposition of Electric Fields (non point charges) o Physics 7D 5 o • o Physics 7D 6 o o • Electric Field Lines o demonstrates the direction of a system of electric fields o an individual electric field is tangent to any point on a line  o electric field lines bunched together means E is strong Physics 7D 7 o field lines can never intersect because their electric field has a unique direction o field maps (cross sections of 3d patterns)  toward -, away from + (duh)  o uniform electric field  • electric dipoles o pair of point charges with equal magnitudes and opposite signs (+/-) o example - water o   the dipole makes it possible to lock molecules in place (Na+, Cl-) o magnitude of dipole moment   magnitude of dipole moment (C*m) = (charge)(distance between them)  the vector of p points toward the + o the net force on an electric dipole in a uniform external electric field always = 0 (not not the torque) o torque of a dipole while in an external electric field Physics 7D 8    magnitude of torque = (magnitude of dipole moment)(magnitude of external electric field)(sin of the angle between p and E)   vector of torque on an electric dipole = cross product of p and E  torque goes through the page (either out of in) and follows the right-hand rule  in the direction of decreasing angle. the dipole (p) wants to be ||with E, AND pointing in the same direction  in the example above, the torque is going into the page (rotating clockwise) o potential energy for a dipole in an electric field   has a min when the angle = 0, pi, etc (||)  has a max when the angle = pi/2, etc (+) o Physics 7D 9 22 Gauss's Law • Flux o the flow through an area o  where the box is imaginary o • calculating o V dot A  where A is the area vector, V is the uniform velocity, or electric field, flowing through that area o  electric flux of a uniform, flat surface = electric field x area (cos(angle)) Physics 7D 10 o o flux is - if the A vector is choosen to point in the opposite direction of E o 1D - linear charge denisty  = charge/length  r^-2 o 2D - surface charge denisty  = charge/area  r^-1 o 3D - volume charge denisty  = charge/volume  r^0 = 1 • Gauss's Law o for a closed spherical surface o   electric flux = enclosed charge/constant  independent of the radius o for any closed surface Physics 7D 11  o moral of the story: for any closed surface  this in in theory. in practice, this is only true for symetircal surfaces o flux is - for a - inside charge (A is pointing the opposite way of E) o  o if the charge is outside the surface, the net flux is always 0 o  • where the chrages lie for solid conductors (metal ball) vs solid insulators (ball of yarn) Physics 7D 12 o o conductor's inside - the net electric field inside a conductor is always zero. If the net electric field were not zero, a current would flow inside the conductor. This would build up charge on the exterior of the conductor. This charge would oppose the field, ultimately (in a few nanoseconds for a metal) canceling the field to zero. • • Physics 7D 13 • • • placing a charge inside a conductor o Physics 7D 14 • Physics 7D 15 23 Electric Potential • electric potential o gravitational potential energy depends on the hight of a mass as electric potential depends on the position of a charge in an electric field • the sign of work done by a force o a + charge is a hill  when you go up the hill, the V and U are positive and the farther they travel the bigger the magnitude o a - charge is a valley  when you go down the valley, the V and U are - and the farther they travel the bigger the magnitude o V - potential  gets smaller when it goes with the E field o U - potential energy  gets smaller when it gets to go where it wants o o work done is conservative  only matters on a to b, not on how it got there  work done is + if it goes with the E field  o reg Physics 7D 16   workd done = (charge)(E field)(distance traveled) o when the force is conservative   U is potential energy  change in energy is - when the work done is positive and something falls to a smaller potential   starting kinetic + potential = ending kinetic + potential • electric potential energy between two point charges o particles, whether + or -, want to accelerate toward lower potential energy o  where r is the distance between them  if the charges have the same sign, then the potential is +, if not, -    this equation is a shared property of both point charges (i.e. there is no electric potential energy of A point charge without a field)  works for spherically symmetric charge distributions (because of Gaussian surfaces, can treat a as its center because that is where all the charge seems to be concentrated anyways) • electric potential energy between more then two point charges Physics 7D 17 o o for total potential between a few point charges o   this is not a vector sum, it is just numbers  ex  • electric POTENTIAL (not energy, just potential) o potential energy that would be associated with a unit charge at a certain point (potential energy per unit charge)   electric potential (Volt) = (potential energy)/(charge) = J/C o  work done per unit charge by an electric force from a to b = (potential at a) - (potential at b) = potential of a with respect to b  this is VOLTAGE!  the difference between the potential at a and the potential at b • electric potential relates to E Physics 7D 18 o  we do initial - final here, where a is initial and b is final o  o electric field units  o Physics 7D 19 • • Physics 7D 20 • • • Physics 7D 21 • • • equipotential surfaces o like contour lines Physics 7D 22 o o because potential energy does not change as a test charge moves over an equipoteitnal surface, the E field doesn't do any work  when E is big, the equipotential surfaces are closer together because the E does a lot of work on a test charge in that small distance o field lines and equipotential surfaces are ALWAYS perpendicular o conductors and equipotential surface at rest  the surface is always an equipotential surface  no potential difference between two points on the surface, V is constant  the insides all have the same potential difference, 'equipotential volume'  the surface charge density on the wall of the cavity is 0 at every point  aka, a hollow metal sphere will hav no charge on the insides, just the outsides • Potential Gradient o used when V is known, but we want to find E o  points in the direction V increases, so E is in the direction V decreases  always perpendicular to the equipotential surface (duh) • Physics 7D 23 24 Capacitance and Dielectrics • capacitor o any two (usually charged) conductors separated by a distance with an insulator (air and vacuums count) between o the conductors are called electrodes o close enough that the Q on one side = the -Q on the other  net charge remains 0  this is the ideal situation, but in rl its not always so o stores energy o has to be induced (have work done on it), like a battery  the voltage difference between a capacitor and a battery for one of each is the same for both the capacitor and the battery • capacitance o  capacitance = charge on one of the conductors/the potential difference between them o SI unti - Farad = 1F = 1C/V o a measure of a capacitor's ability to store energy o for any capacitor in a vacuum, the capacitance only depends on the shapes, dimensions, and separation of the conductors • parallel-plate capacitor o o Physics 7D 24 • • • capacitors in: o series  connected by a single, straight wire  the charge magnitude on the plates are always the same (induced charges, all add up to 0),  the potential difference of each capacitor is not necessarily the same. The individual potential differences add to give the total Physics 7D 25   equivalent capacitance  any number of capacitors lined up in series can be replaced by a single capacitor with the same capacitance 
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