Symbol

Quantity

SI Unit

Comments

A

Magnetic  vector potential

Wb/m

weber/meter

B

Magnetic flux density

T (or Wb/m² )

tesla (or weber/meter² )

B

Susceptance

S

siemen

C

Capacitance

F

farad

C_z

Capacitance per unit length

F/m

farad/meter

D

Electric flux density

C/m²

coulomb/meter²

D

Electric displacement

C/m²

coulomb/meter²

E

Electric field intensity

V/m

volt/meter

F

Force

N

newton

G

Conductance

S

siemen

G_z

Conductance per unit length

S/m

siemen/m

H

Magnetic field intensity

A/m

ampere/meter

I

Current

A

ampere

J

Current density (volume)

A/m²

amperes/meter²

J_s

Current density (surface)

A/m

amperes/meter

K

Surface current density

A/m

ampere/meter

L

Inductance

H

henry

L

Length

m

meter

L_z

Inductance per unit length

H/m

henry/meter

M

Magnetization intensity

A/m

ampere/meter

N

Number of turns

--

dimensionless

P

Electric polarization density

C/m²

coulomb/meter²

P

Power

W

watt

𝓟

Poynting vector

W/m²

watt/meter²

Q

Electric charge

C

coulomb

R

Radial distance

m

meter

R

Resistance

Ω

ohm

R_z

Resistance per unit length

Ω/m

ohm per meter

ℛ

Reluctance

H^-1

henry^-1

S

Area

m²

meter²

S

Standing wave ratio

--

dimensionless ratio

T

One-way propagation coefficient

--

dimensionless ratio

T

Time period

s

second

T

Torque

N·m

newton.meter

U

Energy stored

J

joule

V

Electric potential

V

volt

V

Voltage

V

volt

V_m

Magnetic scalar potential

A

ampere

W

Work, energy

J

joule

X

Reactance

Ω

ohm

Y

Admittance

S

siemen

Z

Impedance

Ω

ohm

Z_o

Characteristic impedance

Ω

ohm

Symbol

Quantity

SI Unit

Comments

a

Unit vector

--

dimensionless

b

Normalized susceptance

--

dimensionless ratio

c

Velocity

m/s

meter/second

c_g

Group velocity

m/s

meter/second

c_o

Velocity of light

m/s

meter/second

c_ph

Phase velocity

m/s

meter/second

d

Length, distance

m

meter

e

Electronic charge

C

coulomb

emf

Electromotive force (emf)

V

volt

f

Frequency

Hz

hertz

f_c

Cut-off frequency

Hz

hertz

g

Normalized conductance

--

dimensionless ratio

i

Current, instantaneous

A

Ampere

k

Wave number

rad/m

radian/meter

k_c

Cut-off wave number

rad/s

radian/second

ℓ

Length

m

meter

m

Magnetic dipole moment

A·m²

ampere.meter²

mmf

Magnetomotive force

A

ampere

n

Index of refraction

--

dimensionless ratio

n

Number of turns per unit length

m^-1

meter^-1

p

Electric dipole moment

C.m

coulomb.meter

q

Electric charge (point)

C

Coulomb

r

Normalized resistance

--

dimensionless ratio

r

Radial distance

m

meter

r

Spherical coordinate distance

m

meter

s

Standing wave ratio

--

dimensionless ratio

t

Time

s

second

tan(δ)

Loss tangent

--

dimensionless

u

parametric variable

varies

varies

v

Velocity

m/s

meter/second

v

voltage, instantaneous

V

volt

v

Volume

m³

meter³

w

Energy density

J/m³

joules/meter³

x

Cartesian coordinate distance

m

meter

x

Normalized reactance

--

dimensionless ratio

y

Cartesian coordinate distance

m

meter

z

Cartesian coordinate distance

m

meter

Symbol

Quantity

SI Unit

Comments

α

Attenuation coefficient

nep/m

neper/meter

β

Phase constant (wave number)

rad/m

radian/meter

γ

Propagation constant

m⁻¹

meter⁻¹

Γ

Reflection coefficient

--

dimensionless ratio

δ

Skin depth

m

meter

ε

Permittivity

F/m

farad/meter

ε_o

Permittivity of free space

F/m

farad/meter

ε_r

Dielectric constant

--

dimensionless ratio

ε_r

Relative permittivity

--

dimensionless ratio

η

Intrinsic impedance

Ω

ohm

θ

Angle of incidence

rad

radian

θ

Spherical coordinate

rad

radian

λ

Wavelength

m

meter

λg

Wavelength in waveguides

m

meter

Λ

Magnetic flux linkage

Wb

weber

μ

Permeability

H/m

henry/meter

μ_o

Permeability of free space

H/m

henry/meter

μ_r

Relative permeability

--

dimensionless ratio

μ^+-

Mobility (electron,  hole)

m²/(V.s)

meter²/(volt·second)

ρ

Cylindrical coordinate radius

m

meter

ρ

Resistivity

Ω.m

ohm.meter

ρ_L

Charge density (linear)

C/m

coulomb/meter

ρ_S

Charge density (surface)

C/m²

coulomb/meter²

ρ_ν

Charge density (volume)

C/m³

coulomb/meter³

ρ

Reflection coefficient, local

--

dimensionless ratio

Ρ

Reflection coefficient phasor, Local

--

dimensionless ratio

σ

Conductivity

S/m

siemen/meter

τ

Time delay

s

second

τ

Transmission coefficient

--

dimensionless ratio

φ

Cylindrical & Spherical coordinate

rad

radian

φ

Phase angle

rad

radian

χ_e

Electric susceptibility

--

dimensionless ratio

χ_m

Magnetic susceptibility

--

dimensionless ratio

ψ_e

Electric flux

C

coulomb

ψ_m

Magnetic flux

Wb

weber

ω

Angular velocity

rad/s

radian/second

ω

Radian frequency

rad/s

radian/second

Symbol

Quantity

Value

SI Unit

Electron charge

e

1.60217733×10⁻¹⁹

C

Electron mass

m

9.1093897×10⁻³¹

kg

Permittivity  of free space

ε_o

8.854187817×10^-12

F/m

Permeability of free space

μ_o

4π×10⁻⁷

H/m

Velocity of light in free space

c_o

2.99792458×10⁸

m/s

intrinsic impedance of free space

η_o

376.7~l20π

ohm

Physical Quantity

UNIT

SYMBOL

Mass

kilogram

kg

Length

meter

m

Time

second

s

Temperature

kelvin

K

Amount of substance

mole

mol

Electric current

ampere

A

Luminous Intensity

candela

cd

Multiplication Factor

Power of 10

Prefix

Symbol

1,000,000,000,000,000,000 = 10⁺¹⁸

+18

exa

E

1,000,000,000,000,000 = 10⁺¹⁵

+15

peta

p

1,000,000,000,000 = 10⁺¹²

+12

tera

T

1,000,000,000  = 10⁺⁹

+9

giga

G

1,000,000 = 10⁺⁶

+6

mega

M

1,000 = 10⁺³

+3

kilo

k

100 = 10⁺²

+2

hecto

h

10 = 10⁺¹

+1

deka

da

0.1 = 10^-1

-1

deci

d

0.01 = 10^-2

-2

centi

c

0.001 = 10^-3

-3

milli

m

0.000,001 = 10^-6

-6

micro

μ

0.000,000,001 = 10^-9

-9

nano

n

0.000,000,000,001 = 10^-12

-12

pico

p

0.000,000,000,000,001 = 10^-15

-15

femto

f

0.000,000,000,000,000,001 = 10^-18

-18

atto

a

Sorted Alphabetically

Sorted Descending

Material

Scientific Format

Engineering Format

Scientific Format

Engineering Format

Material

Aluminum

3.54E+07

35.40E+06

6.17E+07

6.17E+07

Silver

Bakelite

1.00E-09

1.00E-09

5.80E+07

5.80E+07

Copper

Brass

1.57E+07

15.70E+06

4.10E+07

4.10E+07

Gold

Bronze

1.00E+07

10.00E+06

3.54E+07

3.54E+07

Aluminum

Carbon

3.00E+04

30.00E+03

1.82E+07

1.82E+07

Tungsten

Clay

5.00E-03

5.00E-03

1.67E+07

1.67E+07

Zinc

Constantan

2.26E+06

2.26E+06

1.57E+07

1.57E+07

Brass

Copper

5.80E+07

58.00E+06

1.45E+07

1.45E+07

Nickel

Diamond

2.00E-13

200.00E-15

1.03E+07

1.03E+07

Iron

Ferrite  (typical)

1.00E+02

100.00E+00

1.00E+07

1.00E+07

Bronze

Germanium

2.20E+06

2.20E+06

1.00E+07

1.00E+07

Phosphor bronze

Germanium (pure)

2.20E+00

2.20E+00

9.00E+06

9.00E+06

Tin

Glass

1.00E-12

1.00E-12

7.00E+06

7.00E+06

Solder

Gold

4.10E+07

41.00E+06

6.00E+06

6.00E+06

Steel (carbon)

Granite

1.00E-06

1.00E-06

5.00E+06

5.00E+06

Lead

Graphite

7.00E+04

70.00E+03

2.27E+06

2.27E+06

Manganin

Iron

1.03E+07

10.30E+06

2.26E+06

2.26E+06

Constantan

Lead

5.00E+06

5.00E+06

2.20E+06

2.20E+06

Germanium

Limestone

1.00E-02

10.00E-03

1.10E+06

1.10E+06

Steel (stainless)

Manganin

2.27E+06

2.27E+06

1.00E+06

1.00E+06

Mercury

Marble

1.00E-08

10.00E-09

1.00E+06

1.00E+06

Nichrome

Mercury

1.00E+06

1.00E+06

7.00E+04

7.00E+04

Graphite

Mica

1.00E-15

1.00E-15

3.00E+04

3.00E+04

Carbon

Nichrome

1.00E+06

1.00E+06

2.30E+03

2.30E+03

Silicon

Nickel

1.45E+07

14.50E+06

1.00E+02

1.00E+02

Ferrite  (typical)

Oil (transformer)

1.00E-11

10.00E-12

4.00E+00

4.00E+00

Water (sea)

Paraffin

1.00E-15

1.00E-15

2.20E+00

2.20E+00

Germanium (pure)

Phosphor bronze

1.00E+07

10.00E+06

1.00E-02

1.00E-02

Limestone

Polystyrene

1.00E-16

100.00E-18

1.00E-02

1.00E-02

Soil (wet) ~

Porcelain

2.00E-13

200.00E-15

5.00E-03

5.00E-03

Clay

Quartz

1.00E-17

10.00E-18

1.00E-03

1.00E-03

Water (fresh) ~

Rubber

1.00E-15

1.00E-15

4.40E-04

4.40E-04

Silicon (pure)

Silicon

2.30E+03

2.30E+03

1.00E-04

1.00E-04

Soil (dry) ~

Silicon (pure)

4.40E-04

440.00E-06

1.00E-04

1.00E-04

Water (distilled) ~

Silver

6.17E+07

61.70E+06

1.00E-05

1.00E-05

Soil (sandy) ~

Soil (dry) ~

1.00E-04

100.00E-06

1.00E-06

1.00E-06

Granite

Soil (sandy) ~

1.00E-05

10.00E-06

1.00E-08

1.00E-08

Marble

Soil (wet) ~

1.00E-02

10.00E-03

1.00E-09

1.00E-09

Bakelite

Solder

7.00E+06

7.00E+06

1.00E-11

1.00E-11

Oil (transformer)

Steel (carbon)

6.00E+06

6.00E+06

1.00E-12

1.00E-12

Glass

Steel (stainless)

1.10E+06

1.10E+06

2.00E-13

2.00E-13

Diamond

Tin

9.00E+06

9.00E+06

2.00E-13

2.00E-13

Porcelain

Tungsten

1.82E+07

18.20E+06

1.00E-15

1.00E-15

Mica

Water (distilled) ~

1.00E-04

100.00E-06

1.00E-15

1.00E-15

Paraffin

Water (fresh) ~

1.00E-03

1.00E-03

1.00E-15

1.00E-15

Rubber

Water (sea)

4.00E+00

4.00E+00

1.00E-16

1.00E-16

Polystyrene

Wax

1.00E-17

10.00E-18

1.00E-17

1.00E-17

Quartz

Sorted Alphabetically

Sorted Ascending

Material

$\epsilon '$

$\epsilon " / \epsilon '$

$\epsilon '$

$\epsilon " / \epsilon '$

Material

Air

1.0

0.00000

1.0

0.00000

Vacuum

Alcohol (ethyl)

25.0

0.10000

1.0

0.00000

Water (dehydrated)

Aluminum  oxide

8.8

0.00060

1.0

0.00000

Air

Amber

2.7

0.00200

1.0

Carbon dioxide

Ammonia

22.0

1.0

0.00010

Styrofoam

Bakelite

4.7

0.02200

1.5 - 4.0

0.01000

Wood (dry)

Bakelite

5.0

2.0 - 4.0

0.00800

Paper

Barium titanate

1200.0

0.01300

2.1

Petroleum oil

Carbon dioxide

1.0

2.1

0.00030

Teflon

Distilled water

81.0

2.2

Paraffin  wax

Dry soil

2.5 - 3.5

2.3

0.00030

Polypropylene

Dry Soil

2.8 - 4.0

0.05000

2.3

0.00020

Polyethylene

Ferrite (NiZn)

12.4

0.00025

2.3

Oil

Formica

6.0

2.3 - 4.0

0.00200

Rubber

Germanium

16.0

2.5 - 3.5

Dry soil

Glass

4.0 - 7.0

0.00200

2.6

0.00005

Polystyrene

Ice

4.2

0.05000

2.7

0.00200

Amber

Mica

5.4 - 6.0

0.00060

2.8 - 4.0

0.05000

Dry Soil

Neoprene

6.6

0.01100

3.3

0.50000

Snow

Nylon

3.5

0.02000

3.5

0.03000

Plexiglas

Oil

2.3

3.5

0.02000

Nylon

Paper

2.0 - 4.0

0.00800

3.8 - 5.0

0.00075

Quartz

Paraffin  wax

2.2

3.8

0.00075

Silica

Petroleum oil

2.1

4.0 - 7.0

0.00200

Glass

Plexiglas

3.5

0.03000

4.0

0.00060

Pyrex glass

Polyethylene

2.3

0.00020

4.2

0.05000

Ice

Polypropylene

2.3

0.00030

4.4

0.00050

Pyranol

Polystyrene

2.6

0.00005

4.7

0.02200

Bakelite

Porcelain

5.7

0.01400

5.0

Bakelite

Pyranol

4.4

0.00050

5.4 - 6.0

0.00060

Mica

Pyrex glass

4.0

0.00060

5.7

0.01400

Porcelain

Quartz

3.8 - 5.0

0.00075

5.8

0.00300

Steatite

Rubber

2.3 - 4.0

0.00200

5.9

0.00010

Sodium chloride

Seawater

72.0 - 80.0

4.00000

6.0

Formica

Silica

3.8

0.00075

6.6

0.01100

Neoprene

Silicon

11.8

8.8

0.00060

Aluminum  oxide

Snow

3.3

0.50000

11.8

Silicon

Sodium chloride

5.9

0.00010

12.4

0.00025

Ferrite (NiZn)

Steatite

5.8

0.00300

16.0

Germanium

Styrofoam

1.0

0.00010

22.0

Ammonia

Teflon

2.1

0.00030

25.0

0.10000

Alcohol , ethyl

Titanium  dioxide

100.0

0.00150

72.0 - 80.0

4.00000

Seawater

Vacuum

1.0

0.00000

80.0

0.04000

Water (distilled)

Water (dehydrated)

1.0

0.00000

81.0

Distilled water

Water (distilled)

80.0

0.04000

100.0

0.00150

Titanium  dioxide

Wood (dry)

1.5 - 4.0

0.01000

1200.0

0.01300

Barium titanate

Sorted Alphabetically

Sorted Ascending

Material

$\mu '$

$\mu '$

Material

Diamagnetic ≈ 1.0

Diamagnetic ≈ 1.0

Bismuth

0.99983400

0.99983400

Bismuth

Copper

0.99999400

0.99996000

Gold

Gold

0.99996000

0.99997000

Mercury

Mercury

0.99997000

0.99998000

Silver

Paraffin

0.99999942

0.99999200

Water

Sapphire

0.99999976

0.99999400

Copper

Silver

0.99998000

0.99999942

Paraffin

Water

0.99999200

0.99999976

Sapphire

Paramagnetic ≈ 1.0

Paramagnetic ≈ 1.0

Air

1.00000037

1.00000000

Manganese sulfate

Aluminum

1.00002200

1.00000037

Air

Beryllium

1.00000079

1.00000043

Wood

Magnesium

1.00001200

1.00000079

Beryllium

Manganese sulfate

1.00000000

1.00001200

Magnesium

Nickel chloride

1.00004000

1.00002200

Aluminum

Palladium

1.00082000

1.00004000

Nickel chloride

Platinum

1.00026500

1.00008000

Tungsten

Titanium

1.00018000

1.00018000

Titanium

Tungsten

1.00008000

1.00026500

Platinum

Wood

1.00000043

1.00082000

Palladium

Ferromagnetic (nonlinear)

Ferromagnetic (nonlinear)

Carbon Steel

 100.0

 60.0

Cast iron

Cast iron

 60.0

 70.0

Nickel

Cobalt

 100.0

 100.0

Cobalt

Ferrite (typical)

 1,000.0

 100.0

Carbon Steel

Iron (pure)

 5,000.0

 100.0

Powdered iron

Machine steel

 300.0

 300.0

Machine steel

Mild steel

 2,000.0

 1,000.0

Ferrite (typical)

Mumetal

 20,000.0

 2,000.0

Mild steel

Nickel

 70.0

 2,500.0

Permalloy 45

Permalloy 45

 2,500.0

 3,000.0

Transformer iron

Powdered iron

 100.0

5,000.0

Iron (pure)

Purified iron

 200,000.0

 7,000.0

Silicon iron

Sendust

 30,000.0

Mumetal

Silicon iron

 7,000.0

Sendust

Supermalloy

 100,000.0

Supermalloy

Transformer iron

 3,000.0

Purified iron

Maxwell’s Equations

in the Integral Form

in the Point Form

Magnetic Field Circulation

$\oint\overrightarrow{\text{H}}\cdot \text{ }\!\!~\!\!\text{ }\overrightarrow{\text{d}\ell }=\sum {{\text{I}}_{\text{Linkage}}}$

$\vec{\nabla }\times \overrightarrow{\text{H}}=\overrightarrow{\text{J}}$

Electric Field Circulation

$\oint \overrightarrow{\text{E}}\cdot \overrightarrow{\text{d}\ell }=0$

$\vec{\nabla }\times \overrightarrow{\text{E}}=0$

Electric Flux Divergence

$\unicode{x222F}_{\text{S}}\overrightarrow{\text{D}}\cdot \overrightarrow{\text{dS}} =\sum {{\text{Q}}_{\text{enclosed}}}$

$\vec{\nabla }\cdot \overrightarrow{\text{D}}={{\text{ }\!\!\rho\!\!\text{ }}_{\text{v}}}$

Magnetic Flux Divergence

$\unicode{x222F}_{\text{S}}\overrightarrow{\text{B}}\cdot \overrightarrow{\text{dS}} =0$

$\vec{\nabla }\cdot \overrightarrow{\text{B}}=0$

Maxwell’s Equations

in the Integral Form

in the Point Form

Ampere’s Law

Faraday’s Law

$\oint \overrightarrow{\text{E}}\cdot \overrightarrow{\text{d}\ell }=-\iint_{\text{S }\!\!~~\!\!\text{ contoured }\!\!~~\!\!\text{ by }\!\!~~\!\!\text{ C}}\text{ }\!\!~~\!\!\text{ }[\frac{\partial \overrightarrow{\text{B}}}{\partial \text{t}}\cdot \text{dS}]$

$\vec{\nabla }\times \overrightarrow{\text{E}}=-\frac{\partial \overrightarrow{\text{B}}}{\partial \text{t}}$

Gauss’ Law for Electric Flux

$\unicode{x222F}_{\text{S}}\overrightarrow{\text{D}}\cdot \overrightarrow{\text{dS}} =\iiint_{\text{volume }\!\!~~\!\!\text{ enclosed }\!\!~~\!\!\text{ by }\!\!~~\!\!\text{ S}}{{{\text{ }\!\!~~\rho\!\!\text{ }}_{\text{v}}}\,\text{dv}}$

$\vec{\nabla }\cdot \overrightarrow{\text{D}}={{\text{ }\!\!\rho\!\!\text{ }}_{\text{v}}}$

Gauss’ Law for Magnetic Flux

$\unicode{x222F}_{\text{S}}\overrightarrow{\text{B}}\cdot \overrightarrow{\text{dS}} =0$

$\vec{\nabla }\cdot \overrightarrow{\text{B}}=0$

Material Permittivity

$\overrightarrow{\text{D}}=\text{ }\!\!\varepsilon\!\!\text{ }\overrightarrow{\text{E}}$

Material Permeability

$\overrightarrow{\text{B}}=\text{ }\!\!\mu\!\!\text{ }\overrightarrow{\text{H}}$

Material Conductivity

$\overrightarrow{\text{J}}=\text{ }\!\!\sigma\!\!\text{ }\overrightarrow{\text{E}}$

Electrostatic /  Magnetostatic Relationships

Time-Varying Modifications

$\overrightarrow{\text{E}}=-\vec{\nabla }\text{V}$

(5.44)

$\overrightarrow{\text{E}}=-\vec{\nabla }\text{V}-\frac{\partial \overrightarrow{\text{A}}}{\partial ~\text{t}}$

(10.41)

$\overrightarrow{\text{B}}=\vec{\nabla }\times \overrightarrow{\text{A}}$   &    $\vec{\nabla }\cdot \text{ }\!\!~\!\!\overrightarrow{\text{A}}=0$

(8.64)

$\overrightarrow{\text{B}}=\vec{\nabla }\times \overrightarrow{\text{A}}$   & $\text{ }\!\!~\!\!\text{  }\!\!~\!\!\text{ }\vec{\nabla }\cdot \text{ }\!\!~\!\!\overrightarrow{\text{A}}=-\text{ }\!\!\mu\!\!\text{  }~~\!\!\epsilon\!\!\text{ }~\frac{\partial \text{V}}{\partial ~\text{t}}$

(10.46)

${{\nabla }^{2}}\text{V}=-\frac{{{\text{ }\!\!\rho\!\!\text{ }}_{~~\text{v}}}}{\text{ }\!\!\varepsilon\!\!\text{ }}$

(7.3)

${{\nabla }^{2}}\text{V}=-\frac{{{\text{ }\!\!\rho\!\!\text{ }}_{~~\text{v}}}}{\text{ }\!\!\varepsilon\!\!\text{ }}+\text{ }\!\!\mu\!\!\text{  }~~\!\!\epsilon\!\!\text{ }~\frac{{{\partial }^{2}}\text{V}}{\partial {{~\text{t}}^{2}}}$

(10.50)

${{\nabla }^{2}}\overrightarrow{\text{A}}=-\text{ }\!\!\mu\!\!~\overrightarrow{\text{J}}$

(8.68)

${{\nabla }^{2}}\overrightarrow{\text{A}}=-\text{ }\!\!\mu\!\!~\overrightarrow{\text{J}}+\text{ }\!\!\mu\!\!\text{  }~~\!\!\epsilon\!\!\text{ }~\frac{{{\partial }^{2}}\overrightarrow{\text{A}}}{\partial {{~\text{t}}^{2}}}$

(10.47)