UNIT 10
FORMULA SHEET
Gravitational formulae
Electrostatic formulae
Linear motion with constant
acceleration
a
F
=
G
m
1
m
2
r
2
F
=
m
g
, with
g
=
G
M
r
2
F
coul
=
k
q
1
q
2
r
2
F
=
q
E
x
=
x
i
+
v
ix
t
+
1
2
a
x
t
2
v
x
=
v
ix
+
a
x
t
v
2
x
–
v
ix
2
= 2
a
x
(
x
–
x
i
)
Potential:
– G
M
r
Potential:
V
=
U
E
q
=
k
Q
r
F
=
m
v
2
r
Circular motion
Potential energy:
U
g
=
–
G
m
1
m
2
r
(
U
g
= 0 at r =
∞
)
Δ
U
g
=
m g
Δ
h
Potential energy:
U
E
=
k
q
1
q
2
r
(
U
E
= 0 at r =
∞
)
Δ
U
E
=
q
Δ
V
T
2
=
4
π
2
R
3
GM
(Planetary motion)
E
=
k
Q
r
2
Electric field
where
k
=
1
4
πε
0
and
ε
0
= permittivity of free space
E
= –
Δ
V
d
Electric field for parallel plates
τ
=
q d E
sin
θ
Torque on an electric dipole
E
=
Q
ε
0
A
=
σ
ε
0
where
σ
=
Q
A
Electric field for parallel plate capacitor
Φ
E
=
E
⊥
A
=
EA
⊥
=
EA
cos
θ
Electric flux
Φ
E
= 4
π
kq
=
q/
ε
0
Gauss's law
C
=
Q
Δ
V
=
κ
ε
o
A
d
=
κ
A
4
π
kd
Capacitance
where
κ
=
E
o
E
Dielectric constant
E
=
q
κε
0
A
=
σ
κε
0
Electric field for parallel plate capacitor with dielectric
U
=
1
2
Q
Δ
V
=
1
2
C
(
Δ
V
)
2
=
1
2
Q
2
C
Energy stored in a capacitor
Energy density =
Energy
Volume
=
u
=
U
Ad
=
κ
8
π
k
E
2
=
1
2
κε
0
E
2
Constants
G
6.673
×
10
–11
N·m
2
·kg
–
2
m
e
9.109
×
10
–31
kg
M
Earth
5.975
×
10
24
kg
e
1.602
×
10
–19
C
R
Earth
6.371
×
10
6
m
k
8.99
×
10
9
N·m
2
·C
–
2
R
E
orbital
1.50
×
10
11
m
ε
0
8.85
×
10
–12
C
2
·N
–1
·m
–
2

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