16.1) Potential difference and Electrical Potential

  As we learned in Ch. 15,
  
  F = qE
  
  Where F is the Force, q is the charge, and E is the strength of the electric 
  field.
  
  We learned previously that
  
  W = Fd
  
  Where W is Work, F is the Force and d is the distance traveled.
  
  Therefore,
  
  W = Fd = qEd
  
  Where W is Work, F is the Force, d is the distance traveled, q is the charge, 
  and E is the strength of the electric field.
  
  It also follows that
  
  ΔPE = -W = -qEd
  
  The potential difference between two points A and B, VB - VA,
  is defined as the change in potential energy (final value minus initial value)
  of a charge, q, divided by the charge.
  
  ΔV ≡ VB - VA = ΔPE / q
  
  Electric potential is a scalar quantity.
  
  SI units:
  
  1 N/C = 1 V/m
  
  A positive charge gains potential energy when it is moved in a direction
  opposite the electric field.
  
  A negative loses potential energy when it is moved in a direction
  opposite the electric field.
  
  As it gains kinetic energy, it loses an equal amount of electric potential
  energy.
  
  
  
  
16.2) Electric Potential and Potential Energy due to Point Charges
  
  V = keq/r
  
  Where V is the Voltage, ke is a constant 8.99 x 109 Nm2/C2,
  q is the charge, and r is the radius or distance from the charge.
  
  For two charges:
  
  PE = q2V1 = ke q1q2 / r
  
  If the charges have the same sign, PE is positive.  If not, PE is negative.
  
  Conceptually, this means that like charges will repel each other, opposites
  attract.
  
  
 
16.3) Potentials and Charge Conductors

  W = -ΔPE
  
  ΔPE = q(VB - VA)
  
  Therefore
  
  W = -q(VB - VA)
  
  No work is required to move a charge between two points that are at the same 
  potential.
  
  All points on the surface of a charge conductor in electrostatic equilibrium
  are at the same potential.
  
  The electric potential is equal throughout a conductor
  
  The Electron Volt:
  
  The electron volt is defined as the energy that an electron (or proton)
  gains when accelerated through a potential difference of 1 V.
  

16.4) Equipotentials Surfaces

  A surface on which al points are at the same potential is an equipotential
  surface.
  
  No work is required to move a charge at a constant speed on an equipotential
  surface.
  
  These are represented as equipotential line.  (See p. 529).
  
 
7.7) Newton's Universal Law of Gravitation

  Newton deduced from his observations that there must be an attraction between
  all objects with mass in the Universe.  He called it gravity.
  
  Every particle in the Universe attracts every other particle with a force that 
  directly proportional to the product of the masses and inversely proportional 
  to the square of the distance between them.
  
  F = G m1m2/ r2
  
  Where G is a universal constant called constant of universal gravitation.
  
  G = 6.673 x 10 -11 N m2/ kg2
  
  Note: it is impossible to block a gravitational force, it always exists and
  will continue to exist regardless of the boundary between the masses.
  
  Dark Matter
  
  Scientists have observed various bodies of mass in orbit in our Universe.
  They have noticed that in order for certain bodies to stay in their current
  orbit, there must be more mass than we can see.  They call this mass
  dark matter.
  
  Furthermore, the amount of mass in the Universe will dertermine the ultimate
  fate of the Universe.  If there is more than a key amount of mass in the 
  Universe, it will ultimately collapse in on itself.  If there is less, the
  Universe will expand forever.
  
15.10) Electric Flux and Gauss's Law

  Φ = EA
  
  Where Φ is the electric flux, which has the units N m2/C.
  E is the strength of the Electric field, and A is the Area of the surface.
  
  If the surface is not perpendicular to the field, the expression becomes:
  
  Φ = EA cos θ
  
  Where θ is the angle with respect to the field.
  
  For a closed volume surrounded by surface Area A, we shall adopt the 
  convention that flux lines passing into the interior of a volume are negative
  and those passing out are positive.
  
  Gauss's Law:
  
  Φnet = ΣEA cos θ = Q / ε0
  
  Where ε0 is a constant, 8.85 x 10 -12 C2/ Nm2
  
  
  
  

    
  
  

  
HW 11:
p. 517 # 39   
p. 549 MC # 3,4 
p. 550 P # 1
p. 551 # 11