Δ
V
A
B
=
V
A
−
V
B
=
−
∫
A
B
E
→
⋅
d
ℓ
→
{\displaystyle \Delta V_{AB}=V_{A}-V_{B}=-\int _{A}^{B}{\vec {E}}\cdot d{\vec {\ell }}}
E
→
=
−
∂
V
∂
x
i
^
−
∂
V
∂
y
j
^
−
∂
V
∂
z
k
^
=
−
∇
→
V
{\displaystyle {\vec {E}}=-{\tfrac {\partial V}{\partial x}}{\hat {i}}-{\tfrac {\partial V}{\partial y}}{\hat {j}}-{\tfrac {\partial V}{\partial z}}{\hat {k}}=-{\vec {\nabla }}V}
q
Δ
V
{\displaystyle q\Delta V}
U
=
q
V
{\displaystyle U=qV}
P
o
w
e
r
=
Δ
U
Δ
t
=
Δ
q
Δ
t
V
=
I
V
=
e
Δ
N
Δ
t
{\displaystyle Power={\tfrac {\Delta U}{\Delta t}}={\tfrac {\Delta q}{\Delta t}}V=IV=e{\tfrac {\Delta N}{\Delta t}}}
Electron (proton) mass = 9.11×10−31 kg (1.67× 10−27 kg). Elementary charge = e = 1.602×10−19 C.
K
=
1
2
m
v
2
{\displaystyle K={\tfrac {1}{2}}mv^{2}}
kinetic energy . 1 eV = 1.602×10−19 J
V
(
r
)
=
k
q
r
{\displaystyle V(r)=k{\tfrac {q}{r}}}
Many charges:
V
P
=
k
∑
1
N
q
i
r
i
→
k
∫
d
q
r
{\displaystyle V_{P}=k\sum _{1}^{N}{\frac {q_{i}}{r_{i}}}\to k\int {\frac {dq}{r}}}
The alpha-particle is made up of two protons and two neutrons.
Q
=
C
V
{\displaystyle Q=CV}
capacitance .
C
=
ε
0
A
d
{\displaystyle C=\varepsilon _{0}{\tfrac {A}{d}}}
1/2 is gap length of parallel plate capacitor
Series
:
1
C
S
=
∑
1
C
i
.
{\displaystyle {\text{Series}}:\;{\tfrac {1}{C_{S}}}=\sum {\tfrac {1}{C_{i}}}.}
Parallel:
C
P
=
∑
C
i
.
{\displaystyle {\text{ Parallel:}}\;C_{P}=\sum C_{i}.}
u
=
1
2
Q
V
=
1
2
C
V
2
=
1
2
C
Q
2
{\displaystyle u={\tfrac {1}{2}}QV={\tfrac {1}{2}}CV^{2}={\tfrac {1}{2C}}Q^{2}}
stored energy
u
E
=
1
2
ε
0
E
2
{\displaystyle u_{E}={\tfrac {1}{2}}\varepsilon _{0}E^{2}}
