Transcript Electricity So Far…

Electricity So Far…
AP Physics C
Coulomb’s Law and Electric Fields
Due to Point Charges (Ch 21)
• The force between two electric charges
which are motionless (static) is given by
Coulomb’s law
F = kq1q2/r2
• When more than two charges are present,
the force on any one of them can be found
using Coulomb’s law and the principle of
superposition.
Coulomb’s Law and Electric Fields
Due to Point Charges
• The Electric Field is defined as the force
per unit charge
• E = F/Q
• Which also gives us F = EQ
• Electric Field lines
– Out from positive
– In to negative
Electric Field Lines Review
• Rules for drawing electric field lines:
– Electric field lines begin on positive charges (or at infinity) and
end on negative charges (or at infinity)
– The lines are drawn symmetrically entering or leaving an isolated
charge
– The number of lines leaving a positive charge or entering a
negative charge is proportional to the magnitude of the charge
– The density of the lines at any point is proportional to the
magnitude of the field at that point
– At large distances from a system of charges, the field lines are
equally spaced and radial, as if they came from a single point
charge equal to the net charge of the system
– Field lines do not cross
Calculating Electric Fields due to
Continuous Charge Distributions
• The charge distribution is divided into
differential regions whose shapes reflect
the symmetry of the distribution.
Coulomb’s Law and E Fields from
Continuous Charge Distributions
Flux and Gauss' Law
Ch 22
AP Physics C
Gauss’s Law
• Coulomb’s law can be recast into a
different form called Gauss’s law which
provides a very powerful way to find the
electric field when the charge distribution
exhibits a high degree of symmetry, such
as a sphere, cylinder or plane of charge.
Gauss’s Law
• Relates the electric field on a closed
surface to the net charge within the
system
• For static charges, Gauss’s Law and
Coulomb’s Law are EQUIVALENT
• Gauss’s Law: The net number of lines
leaving any surface enclosing the charges
is proportional to the net charge enclosed
by the surface (Qualitative statement)
Gauss’s Law
• Gauss’s law is also of greater validity than
Coulomb’s law as it applies even when
charges move.
How to use Gauss’s Law
(Quantitatively)
•
•
•
•
Count the lines leaving a surface as +
Count the lines entering a surface as –
Figures 22-14 and 22-15 on p.738
But this is only quantitative…how do we
make calculations?
– First we must talk about FLUX
• (It’s what makes time travel possible)
Flux
• Flux, in this case Electric Flux, is the amount of
(electric) field passing through a specified area.
• Think of water flowing in a pipe (flux comes from
the Latin for “flow”)
Electric Flux Φ
• The mathematical quantity that
corresponds to the number of field lines
crossing a surface
• For a surface perpendicular to the Electric
Field, the flux is defined as the product of
the magnitude of the field E and the area
A:
Φ = EA (units are Nm2/C)
Electric Flux Φ continued
• When the area is NOT perpendicular to E,
then the following equation is used:
Φ = EAcosθ = EnA
Where En is the component of E that is
perpendicular or normal to the surface
The box may enclose a charge, by placing a test charge and
observing F, we know E. It is only necessary to do this at the
surface of the shape.
Pictures of
outward (+)
flux and
inward (-)
flux
Situations where the total flux equals zero
The E-field decreases at 1/r2
while the area increases at r2
and that increase and decrease
cancel each other out and that is
why the size of the surface
enclosing Q does not matter.
Electric Flux Φ continued
• What if E varies over a surface? (see Fig
22-18 on p.739)
• If we take very small areas A that can be
considered a plane, we can then sum the
fluxes for each area using Calculus:
 
 E  E  A  EA cos 
 
 E   E  dA
(does not vary)
Quantitative Statement
of Gauss’s Law
• P740
• The net flux through any surface equals
4πk times the net charge inside the
surface (Q)
• OR
• The net flux through any surface equals
the net charge (Q) divided by ε0
Gauss’ Law
  Qenclosed
 E   E  dA 
0
 
Qenclosed
 E  dA   E cos dA   E dA 
0
What we can conclude about Ф
1. Ф is proportional to q
2. Whether Ф is inward or outward
depends on the q inside the surface
3. A q outside the surface offers zero Ф
because Фin = Фout
Gauss’ Law
• The total electric flux through any closed
surface is proportional to the net electric
charge inside the surface
Calculating Electric Flux
• P758 #27-36
Finding a Gaussian Surface
Point Charge
Uniformly charge insulator at a
varying r
Line of Charge
Sheet of Charge
Calculating Electric Fields and Potentials
due to Continuous Charge Distributions
• The electric potential is easier to calculate
because it is a scalar quantity.
• Once the potential is determined, the
electric field can be found by
differentiation.
Coulomb’s Law and Electric Fields
Due to Point Charges
• The electric potential (V) is the electric
potential energy per unit charge, and the
voltage is the difference in potential between
two points in space.
– Recall the magnitude of any form of potential energy
is arbitrary; only differences in potential energy have
meaning.
V   Eds