Formula Sheets: Electrostatics | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE) PDF Download

 Page 1


Formula Sheet for Electrostatics (EMFT) – GATE
1. Basic Concepts
• Electric Charge: Quanti?ed by Coulombs law, q (unit: C).
• Electrostatics: Study of stationary electric charges and ?elds.
• Constants:
– Permittivity of free space: ?
0
= 8.854×10
-12
F/m.
– Coulombs constant: k =
1
4p?
0
˜ 9×10
9
Num
2
/C
2
.
2. Coulombs Law
• Force between Point Charges:
F =
1
4p?
0
q
1
q
2
r
2
ˆ r
where q
1
,q
2
: Charges, r: Distance, ˆ r: Unit vector from q
1
to q
2
.
• Magnitude:
F =
1
4p?
0
|q
1
q
2
|
r
2
3. Electric Field (E)
• De?nition: E =
F
q
0
(force per unit test charge).
• Point Charge:
E =
1
4p?
0
q
r
2
ˆ r
• Superposition Principle:
E
total
=
X
i
E
i
• Continuous Charge Distribution:
E =
1
4p?
0
Z
dq
r
2
ˆ r
4. Electric Potential (V)
• Potential due to Point Charge:
V =
1
4p?
0
q
r
• Potential Di?erence:
V =-
Z
E·dl
1
Page 2


Formula Sheet for Electrostatics (EMFT) – GATE
1. Basic Concepts
• Electric Charge: Quanti?ed by Coulombs law, q (unit: C).
• Electrostatics: Study of stationary electric charges and ?elds.
• Constants:
– Permittivity of free space: ?
0
= 8.854×10
-12
F/m.
– Coulombs constant: k =
1
4p?
0
˜ 9×10
9
Num
2
/C
2
.
2. Coulombs Law
• Force between Point Charges:
F =
1
4p?
0
q
1
q
2
r
2
ˆ r
where q
1
,q
2
: Charges, r: Distance, ˆ r: Unit vector from q
1
to q
2
.
• Magnitude:
F =
1
4p?
0
|q
1
q
2
|
r
2
3. Electric Field (E)
• De?nition: E =
F
q
0
(force per unit test charge).
• Point Charge:
E =
1
4p?
0
q
r
2
ˆ r
• Superposition Principle:
E
total
=
X
i
E
i
• Continuous Charge Distribution:
E =
1
4p?
0
Z
dq
r
2
ˆ r
4. Electric Potential (V)
• Potential due to Point Charge:
V =
1
4p?
0
q
r
• Potential Di?erence:
V =-
Z
E·dl
1
• Electric Field from Potential:
E =-?V
• Superposition:
V
total
=
X
i
V
i
5. Gausss Law
• Integral Form:
I
S
E·dS =
Q
enc
?
0
where Q
enc
: Total charge enclosed by surface S.
• Di?erential Form:
?·E =
?
?
0
where ?: Charge density.
6. Capacitance
• De?nition:
C =
Q
V
• Parallel Plate Capacitor:
C =?
0
A
d
where A: Plate area, d: Separation.
• Capacitors in Series:
1
C
eq
=
1
C
1
+
1
C
2
+···+
1
C
n
• Capacitors in Parallel:
C
eq
=C
1
+C
2
+···+C
n
• Dielectric E?ect:
C =?C
0
, ? =
?
?
0
where ?: Dielectric constant.
7. Electric Field in Conductors and Dielectrics
• Conductor: E = 0 inside, charges reside on surface.
• Dielectric:
D =?E, ? =??
0
• Boundary Conditions:
E
tangential
continuous, D
normal
=s (surface charge)
2
Page 3


Formula Sheet for Electrostatics (EMFT) – GATE
1. Basic Concepts
• Electric Charge: Quanti?ed by Coulombs law, q (unit: C).
• Electrostatics: Study of stationary electric charges and ?elds.
• Constants:
– Permittivity of free space: ?
0
= 8.854×10
-12
F/m.
– Coulombs constant: k =
1
4p?
0
˜ 9×10
9
Num
2
/C
2
.
2. Coulombs Law
• Force between Point Charges:
F =
1
4p?
0
q
1
q
2
r
2
ˆ r
where q
1
,q
2
: Charges, r: Distance, ˆ r: Unit vector from q
1
to q
2
.
• Magnitude:
F =
1
4p?
0
|q
1
q
2
|
r
2
3. Electric Field (E)
• De?nition: E =
F
q
0
(force per unit test charge).
• Point Charge:
E =
1
4p?
0
q
r
2
ˆ r
• Superposition Principle:
E
total
=
X
i
E
i
• Continuous Charge Distribution:
E =
1
4p?
0
Z
dq
r
2
ˆ r
4. Electric Potential (V)
• Potential due to Point Charge:
V =
1
4p?
0
q
r
• Potential Di?erence:
V =-
Z
E·dl
1
• Electric Field from Potential:
E =-?V
• Superposition:
V
total
=
X
i
V
i
5. Gausss Law
• Integral Form:
I
S
E·dS =
Q
enc
?
0
where Q
enc
: Total charge enclosed by surface S.
• Di?erential Form:
?·E =
?
?
0
where ?: Charge density.
6. Capacitance
• De?nition:
C =
Q
V
• Parallel Plate Capacitor:
C =?
0
A
d
where A: Plate area, d: Separation.
• Capacitors in Series:
1
C
eq
=
1
C
1
+
1
C
2
+···+
1
C
n
• Capacitors in Parallel:
C
eq
=C
1
+C
2
+···+C
n
• Dielectric E?ect:
C =?C
0
, ? =
?
?
0
where ?: Dielectric constant.
7. Electric Field in Conductors and Dielectrics
• Conductor: E = 0 inside, charges reside on surface.
• Dielectric:
D =?E, ? =??
0
• Boundary Conditions:
E
tangential
continuous, D
normal
=s (surface charge)
2
8. Energy in Electrostatic Fields
• Potential Energy:
U =
1
2
qV
• Energy Stored in Capacitor:
U =
1
2
CV
2
=
1
2
Q
2
C
=
1
2
QV
• Energy Density:
u =
1
2
?
0
E
2
9. Poissons and Laplaces Equations
• Poissons Equation:
?
2
V =-
?
?
0
• Laplaces Equation (? = 0):
?
2
V = 0
10. Design Considerations
• Symmetry: Use Gausss law for spherical, cylindrical, or planar symmetry.
• Boundary Conditions: Apply at conductor-dielectric or dielectric-dielectric in-
terfaces.
• Applications: Capacitor design, electrostatic shielding, charge distribution anal-
ysis.
• Numerical Methods: Solve Poissons/Laplaces equations for complex geometries.
3