Electric Fields
Charge
- The charge is carried by an electric current of one ampere in one second [C -
Coulombs]
- All charges in nature are multiples of the fundamental electron charge unit:
−19
1. 60 × 10 𝐶
- Scalar quantity:
- Electrons = negative charge
- Protons = positive charge
- Interactions:
- Like charges repel.
- Opposite charges attract.
- When differently charged identical objects touch then separate, they
end up with the same charge: 1) calculate net charge, 2) divide by n
object in contact 3) point 2 = charge of each object after separation
- Uncharged/Neutral object: equal amounts of evenly distributed positive and negative
charges that cancel each other.
- Polarization: charges arrange in groups, creating a net attraction between
oppositely polarized objects. Still, the total net charge of a polarized object is
zero.
- Charged objects: movement of electrons and net amount of positive vs negative
charge determines charge of atom/object
- Gain of electron = negative net charge
- Loss of electron = positive net charge
- Flow of charge:
- Conductors: delocalised valence electrons of atoms in conductor are free to
move in between the structure.
- Conservation of Charge:
- Total net charge in a closed system remains constant.
- Net charge of particles created from energy transformation is zero.
,Electric current
- The rate of flow of electric charge past a cross section of material [A - Amperes]
∆𝑞
- 𝐼= ∆𝑡
, where q is not the # charges, but the magnitude of the net charge.
- Conventional current flows positive → negative, opposite to electrons’ flow.
- In general, an electric current can arise from the flow of either positive or negative
charge carriers.
Drift speed
- Charge carriers: charged particles moving through a material or vacuum.
- Delocalised electrons in conductors:
- Delocalised electrons are the only charge carriers in conductors.
- They normally move randomly through the conductor.
- When a potential difference is applied between the terminals of the conductor:
➔ An electric field is created:
- An electric force acts on the charge carriers
- Charge carriers drift toward the positive (i.e high potential) terminal of
the conductor, in opposite direction to conventional current.
- Drift speed: avg. speed of charge carriers through conductor
−4 −1
(≈ 10 𝑚𝑠 )
- A steady avg. current flows through the conductor: 𝐼 = 𝑛𝐴𝑣𝑞
- q = Charge on each electron
- n = Number of electrons per unit volume (i.e electron density)
- v = drift speed
- t = Time interval for all electrons to pass through A
- A = Cross-sectional area of the conductor
Current in cylinder
- q = each electron’s charge
- n = electron density
- v = avg. drift speed of all electrons
- ∆𝑡 = time interval for all electrons to pass within the cylindrical volume
- A = area of cylindrical volume
- 𝑣∆𝑡 = length of cylindrical volume
→ 𝑉𝐶𝑦𝑙𝑖𝑛𝑑𝑒𝑟 = 𝐴𝑣∆𝑡
∆𝑄
- Tot. net charge in cylinder: ∆𝑄 = 𝑛(𝐴𝑣∆𝑡)𝑞 → ∆𝑡
= 𝑛𝐴𝑣𝑄
∆𝑄
- 𝐼= ∆𝑡
→ 𝐼 = 𝑛𝐴𝑞𝑣
Potential difference / Voltage / Electric Potential
- Work done per unit charge / energy transferred per unit charge between two points in
a conductor [V - Volts]
, 𝑊
- 𝑉= 𝑞
−1
- 1V= 1𝐽𝐶
Electron Volt (eV): amount of energy needed to move an electron through a
potential difference of 1V.
−19
- 1𝑒𝑉 = 1. 6 × 10 𝐽
- Potential Difference:
𝑊𝐴 𝑡𝑜 𝐵
- Between points A and B: 𝑉𝐴 𝑡𝑜 𝐵 = 𝑉𝐵 − 𝑉𝐴 = 𝑞
- Equipotential Points: 𝑉𝐴 𝑡𝑜 𝐵 = 0, no work is done moving between them.
- Positive work is done moving a positive test charge when 𝑉𝐵 > 𝑉𝐴.
-
Work Done and potential energy:
- Work is done when a small charge q is moved in an electric field against the electrical
force.
- Potential difference (i.e energy transferred), is only dependent on the initial
and final position of the test mass.
- Towards Positive Charge:
- Positive test charge moving radially inwards: Positive work due to overcoming
mutual repulsion.
- Negative test charge moving radially outwards: Positive work due to
overcoming mutual attraction.
- Regarding Potential:
- Negative work if a negative test charge moves to a positive potential.
- Negative work if a positive test charge moves to a negative potential.
Kinetic energy:
1 2
- 2
𝑚𝑣 = 𝑒𝑉
Charge
- The charge is carried by an electric current of one ampere in one second [C -
Coulombs]
- All charges in nature are multiples of the fundamental electron charge unit:
−19
1. 60 × 10 𝐶
- Scalar quantity:
- Electrons = negative charge
- Protons = positive charge
- Interactions:
- Like charges repel.
- Opposite charges attract.
- When differently charged identical objects touch then separate, they
end up with the same charge: 1) calculate net charge, 2) divide by n
object in contact 3) point 2 = charge of each object after separation
- Uncharged/Neutral object: equal amounts of evenly distributed positive and negative
charges that cancel each other.
- Polarization: charges arrange in groups, creating a net attraction between
oppositely polarized objects. Still, the total net charge of a polarized object is
zero.
- Charged objects: movement of electrons and net amount of positive vs negative
charge determines charge of atom/object
- Gain of electron = negative net charge
- Loss of electron = positive net charge
- Flow of charge:
- Conductors: delocalised valence electrons of atoms in conductor are free to
move in between the structure.
- Conservation of Charge:
- Total net charge in a closed system remains constant.
- Net charge of particles created from energy transformation is zero.
,Electric current
- The rate of flow of electric charge past a cross section of material [A - Amperes]
∆𝑞
- 𝐼= ∆𝑡
, where q is not the # charges, but the magnitude of the net charge.
- Conventional current flows positive → negative, opposite to electrons’ flow.
- In general, an electric current can arise from the flow of either positive or negative
charge carriers.
Drift speed
- Charge carriers: charged particles moving through a material or vacuum.
- Delocalised electrons in conductors:
- Delocalised electrons are the only charge carriers in conductors.
- They normally move randomly through the conductor.
- When a potential difference is applied between the terminals of the conductor:
➔ An electric field is created:
- An electric force acts on the charge carriers
- Charge carriers drift toward the positive (i.e high potential) terminal of
the conductor, in opposite direction to conventional current.
- Drift speed: avg. speed of charge carriers through conductor
−4 −1
(≈ 10 𝑚𝑠 )
- A steady avg. current flows through the conductor: 𝐼 = 𝑛𝐴𝑣𝑞
- q = Charge on each electron
- n = Number of electrons per unit volume (i.e electron density)
- v = drift speed
- t = Time interval for all electrons to pass through A
- A = Cross-sectional area of the conductor
Current in cylinder
- q = each electron’s charge
- n = electron density
- v = avg. drift speed of all electrons
- ∆𝑡 = time interval for all electrons to pass within the cylindrical volume
- A = area of cylindrical volume
- 𝑣∆𝑡 = length of cylindrical volume
→ 𝑉𝐶𝑦𝑙𝑖𝑛𝑑𝑒𝑟 = 𝐴𝑣∆𝑡
∆𝑄
- Tot. net charge in cylinder: ∆𝑄 = 𝑛(𝐴𝑣∆𝑡)𝑞 → ∆𝑡
= 𝑛𝐴𝑣𝑄
∆𝑄
- 𝐼= ∆𝑡
→ 𝐼 = 𝑛𝐴𝑞𝑣
Potential difference / Voltage / Electric Potential
- Work done per unit charge / energy transferred per unit charge between two points in
a conductor [V - Volts]
, 𝑊
- 𝑉= 𝑞
−1
- 1V= 1𝐽𝐶
Electron Volt (eV): amount of energy needed to move an electron through a
potential difference of 1V.
−19
- 1𝑒𝑉 = 1. 6 × 10 𝐽
- Potential Difference:
𝑊𝐴 𝑡𝑜 𝐵
- Between points A and B: 𝑉𝐴 𝑡𝑜 𝐵 = 𝑉𝐵 − 𝑉𝐴 = 𝑞
- Equipotential Points: 𝑉𝐴 𝑡𝑜 𝐵 = 0, no work is done moving between them.
- Positive work is done moving a positive test charge when 𝑉𝐵 > 𝑉𝐴.
-
Work Done and potential energy:
- Work is done when a small charge q is moved in an electric field against the electrical
force.
- Potential difference (i.e energy transferred), is only dependent on the initial
and final position of the test mass.
- Towards Positive Charge:
- Positive test charge moving radially inwards: Positive work due to overcoming
mutual repulsion.
- Negative test charge moving radially outwards: Positive work due to
overcoming mutual attraction.
- Regarding Potential:
- Negative work if a negative test charge moves to a positive potential.
- Negative work if a positive test charge moves to a negative potential.
Kinetic energy:
1 2
- 2
𝑚𝑣 = 𝑒𝑉
