Physics II: Waves and Electromagnetism
Summary based on Giancoli 4th Edition
Eric Tüschenbönner
May 2019
List of constants
Symbol Value Unit
Permittivity of free space 0 8.85 × 10−12 C 2 /N m2
Elementary charge e 1.60 × 10−19 C
Electron rest mass me 9.11 × 10−31 kg
1
, Chapter 21: Electric Charge and Electric Field
Coulomb’s law
The electric force F acting between two point charges is given by:
1 Qq
F = (1)
4π0 r2
It is proportional to the distance r squared. Moreover, the direction of the force depends on the
sign of the charges - i.e. whether they are both positive/negative or distinct.
Electric field
The electric field E at any point in space is defined as the electric force per unit charge.
~
~ =F
E (2)
q
The electric field at a distance r from a point charge is given by:
1 Q
E= (3)
4π0 r2
It only depends on the charge which generates the electric field, not on the test charge.
For specific geometries:
1
• Point charge: E ∝ r2
1
• Infinite line of charge: E ∝ r
• Infinite plane of charge: E independent of r
The following variables are often used to indicate geometric charge distributions:
• λ [C/m]: charge per unit length
• σ [C/m2 ]: charge per unit area
• ρ [C/m3 ]: charge per unit volume
Continuous charge distributions
The electric potential of geometric charge distributions can be found by integration. The process
always starts of with the following formula:
Z
1 dQ
E= (4)
4π0 r2
Long line of charge
1 λ
E= (5)
2π0 x
2
Summary based on Giancoli 4th Edition
Eric Tüschenbönner
May 2019
List of constants
Symbol Value Unit
Permittivity of free space 0 8.85 × 10−12 C 2 /N m2
Elementary charge e 1.60 × 10−19 C
Electron rest mass me 9.11 × 10−31 kg
1
, Chapter 21: Electric Charge and Electric Field
Coulomb’s law
The electric force F acting between two point charges is given by:
1 Qq
F = (1)
4π0 r2
It is proportional to the distance r squared. Moreover, the direction of the force depends on the
sign of the charges - i.e. whether they are both positive/negative or distinct.
Electric field
The electric field E at any point in space is defined as the electric force per unit charge.
~
~ =F
E (2)
q
The electric field at a distance r from a point charge is given by:
1 Q
E= (3)
4π0 r2
It only depends on the charge which generates the electric field, not on the test charge.
For specific geometries:
1
• Point charge: E ∝ r2
1
• Infinite line of charge: E ∝ r
• Infinite plane of charge: E independent of r
The following variables are often used to indicate geometric charge distributions:
• λ [C/m]: charge per unit length
• σ [C/m2 ]: charge per unit area
• ρ [C/m3 ]: charge per unit volume
Continuous charge distributions
The electric potential of geometric charge distributions can be found by integration. The process
always starts of with the following formula:
Z
1 dQ
E= (4)
4π0 r2
Long line of charge
1 λ
E= (5)
2π0 x
2
