Download AP Physics Chapter 25-26 Key Equations and Ideas Electric

AP Physics Chapter 25-26 Key Equations and Ideas
Electric Potential Energy & Potential
U = qV
U = qV
kQ
(single charge)
V
r
n
V
n
V
 k
i
i 1
Qi
r
i 1
i
U = -W
kQ1 Q2
U
r
(n charges)
1 1 
W  U  kQ1Q2    (Q1 A  B in Q2 field)
 rB rA 
dQ
Wexternal = -WE-field
V  dV  k
r
 
dV
V
(Ecap = )
V   E  dr  E  
dx
d



V = constant inside a conductor
Conductors in contact are at an equipotential
Capacitance
 A
C o
d
L
C  2o
b
ln  
a
C  4o
C  4o a
Ceq 
C
i
i 1
parallel

(parallel plate)
(cylindrical)
(spherical)
(sphere)
n
1

Ceq
n
 C1
i 1
i
series
1 Q2
1
1

CV 2 
QV
2 C
2
2
u = ½oE2 (energy density)
U 
C = Co
Key Ideas:
ab
ba
Q = CV
E
E o

E
V
d
Electric potential energy is analogous to gravitational potential energy. It is a property of
an electric field, regardless of whether a charged particle has been placed into the field
or not. It is an energy of a charged body in an external field (or more precisely, the
energy of the system consisting of the body and the external electric field).

Equipotential surfaces (real or imaginary) have the same electric potential at all points.

The change of potential or potential energy of a particle is independent of the path taken.
The potential difference between any two points in an electric field can be found by
 
integrating E  ds along a path connecting the two points.

A positively charged particle produces a positive electric potential. A negatively charged
particle produces a negative electric potential. You move to higher potential when you
move closer to a positive charge.

Electric potential is a scalar. The electric potential from discrete charges can be found by
simply summing up the contribution from each charge. You must integrate when you have a
continuous distribution of charge.

The component of the electric field in any direction is the negative of the rate of change
of the electric potential with distance in that direction (i.e. the partial derivative).

The electric potential energy of a system of fixed point charges is equal to the work that
must be done by an external agent to assemble the system, bringing each charge in from
an infinite distance.

An excess charge placed on an isolated conductor will distribute itself on the surface of
that conductor so that all points of the conductors, whether on the surface or in the
interior, come to the same potential. This is true even if the conductor has an internal
cavity and even if that cavity contains a net charge.

A capacitor is a device where electric potential energy can be stored. Capacitance is the
ratio of how much charge can be stored in a capacitor and the potential difference
between the two conductors.

When a potential difference is applied across several capacitors connected in parallel, that
potential difference is applied across each of the individual capacitors. The total charge
stored on the capacitors is the sum of the charges stored on each of the individual
capacitors.

Capacitors connected in parallel can be replaced with an equivalent capacitor that has the
same total charge and the same potential difference as the actual parallel capacitors.

When a potential difference is applied across several capacitors connected in series, the
capacitors have identical charges. The sum of the potential differences across each of
the individual capacitors is equal to the overall applied potential difference.

Capacitors connected in series can be replaced with an equivalent capacitor that has the
same total charge and the same potential difference as the actual series capacitors.

When a circuit has capacitors connected in both parallel and series, begin by finding the
equivalent capacitance of the parallel capacitors and the equivalent capacitance of the
series capacitors. Take the problem step by step until you have an equivalent capacitance
for the entire circuit.

The potential energy of a charged capacitor may be viewed as being stored in the electric
field between its plates.

In a region completely filled by a dielectric material of dielectric constant , all
electrostatic equations containing 0 can be modified by replacing 0 with 0. The
capacitance increases by a factor of . The electric field decreases by a factor of .