Fysica Electricity and Magnetism
CH21 Electric fields
Unlike charges attract, like charges repel
Law of conservation: net amount of electrical charge created = 0
An Ion is an atom with a positive or negative charge
Polar atoms have an uneven distribution of charge although they are neutral
A conductor is a material than enables movement of charge (they have some loosely bounded
electrons from nuclei which is why electrons can move)
Insulators are materials that don’t enable the movement of charge (they have tightly bonded
electrons)
Semiconductors (silicon and germanium) are intermediate of insulators and conductors
Induction: separation of charges within an object without touching them, the net change in
charge is equal to zero, but there is separation.
An electroscope or electrometers is an object which can be used for the detection of charge
Q1 Q2
1. Coulombs Law: F=k
r2
F= Force (N), k= 9.0* 109 Nm2C-2, Q=charge (C)
2. Charge of an electron e=1.602∗10−19 C
Electric charge is quantized, because an object cannot gain or lose a fraction of an electron
1
∗Q 1 Q 2
3. Coulombs law with permittivity of free space: 4 π ϵ0 (precise for all point
F= 2
r
charges)
F
⃗
E=
4. Electric field: ⃗
q
, kqQ 1
5. Electric field for a single point charge: F
⃗
E= =
⃗
( r ) =
k∗Q 4 π ϵ
=
∗Q
. E is depended 2
0
2 2
q q r r
of Q (the charge Q that produces the field)
1
∗dQ
6. Charge distributed continuously: 4 π ϵ0 and E=∫ dE
dE= 2
r
Electric field lines of a point charge distribute radially, and this can be inward or outwards
depending on the test charge.
A dipole is a combination of two equal charges of the opposite sign.
Properties of field lines:
- Electric field lines indicate the direction of electric field, the field points in a direction
tangent to de field lines
- The lines are drawn so that E is proportional to the number of lines
- Electric field lines start on positive charges and end on negative charges.
- They never cross, because the field cannot have multiple directions or work multiple
forces on a test charge.
- Electric field lines can never intersect.
- Electric field lines point away from positive charges and toward negative charges.
- At every point in space, the electric field vector at that point is tangent to the electric field line through that point.
Properties of conductors:
- E inside a conductor = 0 in static situation
- Any net charge of a conductor distributes itself on the surface of the conductor
- Although there is not field within a conductor, there is one outside of it
- The electric field is always perpendicular to the surface of the conductor
F =q ⃗
7. Force of an electric field on an object: ⃗ E
A dipole moment is represented by p from which the quantity Ql. Because of this, there can be
a torque on molecules.
8. Torque on polar molecules: τ = p × E
, CH22 Electrical Flux
Qencl
E∙d ⃗
9. Gauss law: ∮ ⃗ A=
ϵ0
An electric flux is the concept an electric field passing through an area.
10. Electric flux: Φ=E⊥∗A=E∗A⊥ =E A cos ( θ )
The area A can also be represented as vector ⃗ A with magnitude A whose direction is
perpendicular to the electric field. This results in:
11. Φ=⃗ E∙⃗A
Flux entering an enclosed volume is negative, flux leaving an enclosed volume must be positive.
If all electric field lines that enter an enclosed volume also leave the volume, the net total flux
will be zero. The net total flux will only be nonzero whenever electric field lines start or stop
within the enclosed volume.
Gauss law is the exact relation between an enclosed volume and an electric field.
Qencl
E∙d ⃗
12. Gauss law: ∮ ⃗ A=
ϵ0
With Qencl as the net charge enclosed by the surface.
Electric fields can be produced by static electric charges, Coulombs law describes this.
They can however also be produced by changing magnetic field, this can’t be described
by Gauss law, but can be described by Gauss law, thus Gauss laws true for all electric
fields. This is why Gauss law is viewed as a more general law than Coulombs law.
E∙d ⃗
Gauss law can also be described by using k which gives ∮ ⃗ A =4 πkQ which is more
complicated than by using the permittivity constant as seen in 12.
Q encl Q Q 1 Q encl
E∙d ⃗
Calculation ex.22-3: ∮ ⃗ A= →⃗ A = encl → E∙ ( 4 π r 2) = encl → E=
E∮ d ⃗
ϵ0 ϵ0 ϵ0 ( 4 π r 2) ϵ 0
Qencl σAA σA
E∙d ⃗
13. Electric field near any conducting field: ∮ ⃗ A= → EA= → E=
ϵ0 ϵ0 ϵ0
Net charge within a conductor will always be equal to 0.
CH21 Electric fields
Unlike charges attract, like charges repel
Law of conservation: net amount of electrical charge created = 0
An Ion is an atom with a positive or negative charge
Polar atoms have an uneven distribution of charge although they are neutral
A conductor is a material than enables movement of charge (they have some loosely bounded
electrons from nuclei which is why electrons can move)
Insulators are materials that don’t enable the movement of charge (they have tightly bonded
electrons)
Semiconductors (silicon and germanium) are intermediate of insulators and conductors
Induction: separation of charges within an object without touching them, the net change in
charge is equal to zero, but there is separation.
An electroscope or electrometers is an object which can be used for the detection of charge
Q1 Q2
1. Coulombs Law: F=k
r2
F= Force (N), k= 9.0* 109 Nm2C-2, Q=charge (C)
2. Charge of an electron e=1.602∗10−19 C
Electric charge is quantized, because an object cannot gain or lose a fraction of an electron
1
∗Q 1 Q 2
3. Coulombs law with permittivity of free space: 4 π ϵ0 (precise for all point
F= 2
r
charges)
F
⃗
E=
4. Electric field: ⃗
q
, kqQ 1
5. Electric field for a single point charge: F
⃗
E= =
⃗
( r ) =
k∗Q 4 π ϵ
=
∗Q
. E is depended 2
0
2 2
q q r r
of Q (the charge Q that produces the field)
1
∗dQ
6. Charge distributed continuously: 4 π ϵ0 and E=∫ dE
dE= 2
r
Electric field lines of a point charge distribute radially, and this can be inward or outwards
depending on the test charge.
A dipole is a combination of two equal charges of the opposite sign.
Properties of field lines:
- Electric field lines indicate the direction of electric field, the field points in a direction
tangent to de field lines
- The lines are drawn so that E is proportional to the number of lines
- Electric field lines start on positive charges and end on negative charges.
- They never cross, because the field cannot have multiple directions or work multiple
forces on a test charge.
- Electric field lines can never intersect.
- Electric field lines point away from positive charges and toward negative charges.
- At every point in space, the electric field vector at that point is tangent to the electric field line through that point.
Properties of conductors:
- E inside a conductor = 0 in static situation
- Any net charge of a conductor distributes itself on the surface of the conductor
- Although there is not field within a conductor, there is one outside of it
- The electric field is always perpendicular to the surface of the conductor
F =q ⃗
7. Force of an electric field on an object: ⃗ E
A dipole moment is represented by p from which the quantity Ql. Because of this, there can be
a torque on molecules.
8. Torque on polar molecules: τ = p × E
, CH22 Electrical Flux
Qencl
E∙d ⃗
9. Gauss law: ∮ ⃗ A=
ϵ0
An electric flux is the concept an electric field passing through an area.
10. Electric flux: Φ=E⊥∗A=E∗A⊥ =E A cos ( θ )
The area A can also be represented as vector ⃗ A with magnitude A whose direction is
perpendicular to the electric field. This results in:
11. Φ=⃗ E∙⃗A
Flux entering an enclosed volume is negative, flux leaving an enclosed volume must be positive.
If all electric field lines that enter an enclosed volume also leave the volume, the net total flux
will be zero. The net total flux will only be nonzero whenever electric field lines start or stop
within the enclosed volume.
Gauss law is the exact relation between an enclosed volume and an electric field.
Qencl
E∙d ⃗
12. Gauss law: ∮ ⃗ A=
ϵ0
With Qencl as the net charge enclosed by the surface.
Electric fields can be produced by static electric charges, Coulombs law describes this.
They can however also be produced by changing magnetic field, this can’t be described
by Gauss law, but can be described by Gauss law, thus Gauss laws true for all electric
fields. This is why Gauss law is viewed as a more general law than Coulombs law.
E∙d ⃗
Gauss law can also be described by using k which gives ∮ ⃗ A =4 πkQ which is more
complicated than by using the permittivity constant as seen in 12.
Q encl Q Q 1 Q encl
E∙d ⃗
Calculation ex.22-3: ∮ ⃗ A= →⃗ A = encl → E∙ ( 4 π r 2) = encl → E=
E∮ d ⃗
ϵ0 ϵ0 ϵ0 ( 4 π r 2) ϵ 0
Qencl σAA σA
E∙d ⃗
13. Electric field near any conducting field: ∮ ⃗ A= → EA= → E=
ϵ0 ϵ0 ϵ0
Net charge within a conductor will always be equal to 0.
