physics
G
If qs>0, then dir E is away from qs.
G
If qs<0, then dir E is toward qs.
qs
“electric
charge”
scalar
unit=C
Gauss’s Law:
G
G
∫ E • dA =
net q enclosed
ε0
G
For a uniform E which is perpendicular to
| net q enclosed |
the Gaussian surface: E A =
ε0
kq
Point source: E = 2s (Coulomb’s Law)
r
electric field and electric force
G
E at a point in space
“electric field”
vector; unit = N/C
G
The E at a point in space
G
indicates what the F would
be on a +1C q0 at that point
in space.
G
G
If q0>0, then dir E =dir F .
G
G
If q0<0, then dir E is opposite to dir F .
F = E q 0
For point charges or nonoverlapping
spherically symmetrical charge
distributions:
kq q
F = 12 2 (Coulomb’s Law)
r
G
F on q0
“electric
force”
vector
unit=N
Spherical symmetry:
Q
kQ
Outside: E =
=
4πε 0 r 2 r 2
kQ r
Inside uniformly charged sphere: E = 3
R
Inside hollow sphere: E=0
Line symmetry: Outside: E =
λ
2πε 0 r
Inside hollow pipe: E=0
σ
Plane symmetry: Outside: E =
2ε 0
1
1
. Units for λ are C/m. Units for σ are C/m2. Units for ρ (not shown in chart) are C/m3.
k=
, ε0 =
4πε 0
4πk
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physics
qs
“electric
charge”
scalar
unit=C
kq s
r
This formula
works for a point
source, or outside
a spherically
symmetric charge
distribution.
V=
electric potential energy and electric potential
V at a point in space
“electric potential”
U = Vq0
U of q0,qs system
“electric potential energy”
scalar; unit=volt=J/C
scalar; unit=J
The V at a point in space indicates what the U
would be for a +1C q0 at that point in space;
i.e., the V at a point in space indicates how
much work it would take to move a +1C q0
from ∞ to that point in space.
For point charges or
nonoverlapping
spherically symmetric
charge distributions:
kq q
U= 1 2
r
The U of a system of charges
indicates how much work it
would take to move the
charges from ∞ to their
present positions.
For q0>0, V is like “height”.
For q0<0, V is like “depth”.
“electric
charge”
scalar
unit=C
electric potential difference and change in electric potential energy
∆U of q0,qs system
∆V between two points in space
G
B
“electric potential difference”, “voltage”
G
∆U = ∆V ⋅ q0 “change in electric
= − ∫ E • dr
potential energy”
The symbol “V” is often used to mean “∆V”.
A
G
E
qs
∆V AB
G
E points from high V to low V,
indicating the sign of ∆V.
G
For constant E : ∆V = E || ⋅ ∆r
For point sources, or outside
spherically symmetric charge
distributions:
kq
kq
∆V AB = s − s
rB
rA
scalar; unit=volt=J/C
scalar; unit=J
The ∆V between two points in space indicates
what the ∆U would be for a +1C q0 moving
between those two points in space;
i.e., the ∆V between two points in space
indicates how much work it would take to move
a +1C q0 between those two points in space.
The ∆U of a system of
charges indicates how
much work it took to
move the charges from
their previous positions
to their present
positions.
For q0>0, ∆V is like “change in height”.
For q0<0, ∆V is like “change in depth”.
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