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Electrostatics
Electricity and Magnetism
Objectives
Objectives
Objectives
BACKGROUND
Electron flow
Electricity in wires is a flow of electrons along the wire
from the negative end of the battery to the positive end
What do we call this flow of electrons? Electrical current
7 of 38 © Boardworks Ltd 2007
The other electricity
Where can electricity be found in this lab scene?
8 of 38 © Boardworks Ltd 2007
What do the following familiar events have in common?
Static Electricity
 A lightning strike.
 Dusters that attract dust.
 Crackles when combing hair.
 Cling film sticking to your hands.
 Dust being attracted to television screens.
 Clothes clinging to each other in a dryer.
 Getting a shock after rubbing your feet on
a carpet and then touching a metal object.
All these events are due to static electricity.
What causes static electricity to occur?
9 of 38 © Boardworks Ltd 2007
What is static electricity?
Static electricity is due to the
build up of electric charge.
Sometimes, after walking on
a carpet and then touching a
metal object, such as a door
knob, you might get a small
shock. This is caused by
static electricity.
It is called ‘static’ electricity
because the charge is unable
to flow.
The build up of electric charge
can cause dangerous sparks.
10 of 38 © Boardworks Ltd 2007
Lightning is an electric
discharge that occurs when
charge builds up in clouds.
Is lightning caused by electric charge?
The physical properties of
water enables regions of a
cloud to become positively-
or negatively-charged.
When enough charge has
built up, it will follow a path
to Earth.
This movement produces
lightning, which is simply
a big spark!
11 of 38 © Boardworks Ltd 2007
Charges and electric fields
An object is said to be ‘charged’ if it has an imbalance in
positive and negative charges. In most cases, this is due to
the addition or removal of electrons.
Static electricity is a build-up of
electric charge on the surface of
an object due to the removal or
addition of electrons, commonly
caused by friction.
A Van der Graaff generator
uses a rubber belt rubbing
against metal points to create a
build-up of charge on the surface
of a hollow metal sphere.
12 of 5 © Boardworks Ltd 2011
How does static charge build up?
Static charge can build up when two
insulating materials are rubbed
together, such as a plastic comb
moving through hair.
Friction between the materials causes
electrons to be transferred from one
material to the other:
 one material ends up with more electrons, so it
now has an overall negative charge
 one material ends up with fewer electrons, so it
now has an overall positive charge.
13 of 5 © Boardworks Ltd 2011
All materials are made of atoms, which contain electric charges.
An atom has equal numbers of electrons and protons and so has no
overall charge.
Around the outside
of an atom are
electrons, which
have a negative
charge.
The nucleus at the
centre of an atom
contains protons,
which have a positive
charge.
Electrons do not always stay attached to atoms and can
sometimes be removed by rubbing.
Where does static charge come from?
15 of 38 © Boardworks Ltd 2007
Static electricity has many uses, including:
How can static electricity be used?
 photocopiers
and laser
printers
 filtering
factory
smoke
 spray painting cars
 heart
defibrillators
ELECTRIC FIELDS
17 of 36 © Boardworks Ltd 2010
What is electric charge?
Electric charge is a feature of certain elementary particles,
such as electrons and protons, that causes them to interact
with each other.
The unit of electric charge is the coulomb, C. One coulomb
is equivalent to the charge transported by 1 ampere of
current in 1 second.
 Protons have an electric charge of 1.60 × 10-19 C (e).
 Electrons have an electric charge of -1.60 × 10-19 C (-e).
Like charges repel; unlike charges attract.
18 of 36 © Boardworks Ltd 2010
Charges and electric fields
All charged objects are surrounded by a region called an
electric field.
An electric field is a region where a
charged particle will experience a force.
Electric fields can be represented by electric field lines.
● The direction of the lines represents the direction of the
field – it shows the direction a positive charge would move
in the field.
● The distance between lines represents the strength of
the field – the closer the lines, the stronger the field.
Electric field
21 of 36 © Boardworks Ltd 2010
Charged particle interactions
Interaction of charges
Interaction of charges continued
COULOMB’S LAW
26 of 36 © Boardworks Ltd 2010
Coulomb’s experiments
In 1783, the French physicist Charles Augustin de Coulomb
measured the electrostatic force between two electric charges.
He deduced that the magnitude of the force, F, between
charges Q1 and Q2 is:
 proportional to the product of Q1 and Q2 (i.e. Q1 × Q2)
 inversely proportional to the square of the distance (r)
between them.
This forms the basis of Coulomb’s law.
27 of 36 © Boardworks Ltd 2010
Coulomb deduced
that:
where k is a constant
of proportionality:
Coulomb’s law
εo is the permittivity of free space:
8.85 × 10-12 C2 N-1 m-2 (or 8.85 × 10-12 Fm-1)
4πεo
1 Q1Q2
r2
F =
4πεor2
Q1Q2
F =
or
or:
4πεo
1
k =
r2
Q1Q2
F 
r2
kQ1Q2
F =
So Coulomb’s law can be stated as:
29 of 36 © Boardworks Ltd 2010
Coulomb’s law: true or false?
30 of 36 © Boardworks Ltd 2010
ELECTRIC FIELD STRENGTH
Electricity and Magnetism
31 of 36 © Boardworks Ltd 2010
Placing a charge in an electric field
32 of 36 © Boardworks Ltd 2010
Electric field strength
Electric field strength is defined as the force experienced
per unit charge. The charge in the equation refers to the
charge of the particle in the field.
electric field strength = force / charge
E = F / Q
Example: What is the electric field strength around a
point charge if a 3.20 × 10-19 C charge experiences a
force of 7.30 × 10-15 N?
E = (7.30 × 10-15 ) / (3.20 × 10-19 )
E = 2.28 × 104 NC-1
E = F / Q
33 of 36 © Boardworks Ltd 2010
Electric field strength: uniform fields
The electric field between two parallel plates (e.g. capacitor
plates) is uniform: a charge will experience the same force
wherever it is placed between the plates.
The electric field strength
depends on two factors:
the voltage between the
plates and the distance
between them.
electric field strength = voltage / distance
E = V / d
The units of E in this instance are volts per metre (Vm-1).
34 of 36 © Boardworks Ltd 2010
Electric field strength: radial fields
35 of 36 © Boardworks Ltd 2010
Electric field strength vs distance for a
sphere
For the case of sphere of
radius a.
38 of 36 © Boardworks Ltd 2010
Zero values of E between two charges (1)
In the case of two positive or two negative point charges, there
is a point along the line between the two charges where the
electric field strength is zero. Can you explain why?
E is a vector quantity that acts in the same direction as the
force on a positive charge placed in the field. Therefore the
strength of each field will be equal and opposite at some point
along the line above, and the vector sum will be zero.
Where will that point be in the above example if Q1 = 2Q2?
39 of 36 © Boardworks Ltd 2010
Zero values of E between two charges (2)
When E is 0: E1 = E2
At what point will E be
zero if Q1 = 2Q2?
Substitute in equations for E: Q1/4πεor1
2 = Q2/4πεor2
2
Cancel constants: Q1/r1
2 = Q2/r2
2
Q1 = 2Q2 so: 2Q2/r1
2 = Q2/r2
2
Cancel Q2 values from each side: 2 = r1
2/r2
2
Square root each side: √2 = r1/r2
Multiply both sides by r2: r1 = r2√2
40 of 36 © Boardworks Ltd 2010
Zero values of E between two charges (3)
r1 = r2√2
At what point will E be
zero if Q1 = 2Q2?
This means that the point lies along the line further
from Q1 than from Q2.
The exact distance can be calculated if necessary by
working out the fraction of the total distance r1 and r2
make up:
 r1 is √2/(1+√2) of the total distance from Q1
 r2 is 1/(1+√2) of the total distance from Q2.
41 of 36 © Boardworks Ltd 2010
ELECTRIC POTENTIAL
Electricity and Magnetism
Electric potential vs potential difference
43 of 36 © Boardworks Ltd 2010
What is electric potential?
If a positive test charge is moved from infinity to a position in
an electric field, the electric potential energy (Ep) of that
charge will change. In other words work is done on the charge.
electric field
Zero Ep can be set anywhere, but in electric fields around a
point charge it is set at infinity. This is because the strength of
the field would also be zero at infinity.
positive
test charge
at infinity
44 of 36 © Boardworks Ltd 2010
What is electric potential?
Rearranging gives:
The electric potential at a certain position in an electric field
is the work done per unit positive charge when a positive test
charge is moved from infinity to that position.
electric potential energy = electric potential × charge
Ep = QV
V = Ep / Q
electric potential = electric potential energy / charge
In other words, electric potential is voltage, and is measured
in volts (V) or joules per coulomb (JC-1).
Electric potential of point charge
47 of 36 © Boardworks Ltd 2010
Electric potential and radial fields
The electric potential, V, near a point charge, Q, at a
distance r is given by the formula:
4πεor
Q
V =
Example: What is the electric potential at a distance of
20.0mm around a point charge of 1.40 × 10-8 C?
V = 6294V
4πεor
Q
V =
1.40 × 10-8
4 × π × (8.85 × 10-12) × 0.02
V =
Electric potential due to multiple
charges
Vector addition also applies for electric field strengths
Relationship between Electric field and
potential
53 of 36 © Boardworks Ltd 2010
Equipotentials
54 of 36 © Boardworks Ltd 2010
Potential gradients
55 of 36 © Boardworks Ltd 2010
Electric fields: equations summary
SPECIFIC APPLICATIONS
Charged conducting sphere
Inside a charged conducting
sphere the electric field is zero
due to equilibrium, the potential
remains constant at the value it
reaches at the surface
Outside of the sphere the electric
field environment is identical to
that of a point charge. Therefore
the potential is the same as that
of a point charge:
CLASSWORK
ANSWERS:
1. C
2. B
3. E
4. C
Physics Chapter Three - Electric Fields and Charges
Physics Chapter Three - Electric Fields and Charges
Physics Chapter Three - Electric Fields and Charges
Physics Chapter Three - Electric Fields and Charges
Physics Chapter Three - Electric Fields and Charges
Physics Chapter Three - Electric Fields and Charges
Physics Chapter Three - Electric Fields and Charges
Physics Chapter Three - Electric Fields and Charges

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Physics Chapter Three - Electric Fields and Charges

  • 6. Electron flow Electricity in wires is a flow of electrons along the wire from the negative end of the battery to the positive end What do we call this flow of electrons? Electrical current
  • 7. 7 of 38 © Boardworks Ltd 2007 The other electricity Where can electricity be found in this lab scene?
  • 8. 8 of 38 © Boardworks Ltd 2007 What do the following familiar events have in common? Static Electricity  A lightning strike.  Dusters that attract dust.  Crackles when combing hair.  Cling film sticking to your hands.  Dust being attracted to television screens.  Clothes clinging to each other in a dryer.  Getting a shock after rubbing your feet on a carpet and then touching a metal object. All these events are due to static electricity. What causes static electricity to occur?
  • 9. 9 of 38 © Boardworks Ltd 2007 What is static electricity? Static electricity is due to the build up of electric charge. Sometimes, after walking on a carpet and then touching a metal object, such as a door knob, you might get a small shock. This is caused by static electricity. It is called ‘static’ electricity because the charge is unable to flow. The build up of electric charge can cause dangerous sparks.
  • 10. 10 of 38 © Boardworks Ltd 2007 Lightning is an electric discharge that occurs when charge builds up in clouds. Is lightning caused by electric charge? The physical properties of water enables regions of a cloud to become positively- or negatively-charged. When enough charge has built up, it will follow a path to Earth. This movement produces lightning, which is simply a big spark!
  • 11. 11 of 38 © Boardworks Ltd 2007 Charges and electric fields An object is said to be ‘charged’ if it has an imbalance in positive and negative charges. In most cases, this is due to the addition or removal of electrons. Static electricity is a build-up of electric charge on the surface of an object due to the removal or addition of electrons, commonly caused by friction. A Van der Graaff generator uses a rubber belt rubbing against metal points to create a build-up of charge on the surface of a hollow metal sphere.
  • 12. 12 of 5 © Boardworks Ltd 2011 How does static charge build up? Static charge can build up when two insulating materials are rubbed together, such as a plastic comb moving through hair. Friction between the materials causes electrons to be transferred from one material to the other:  one material ends up with more electrons, so it now has an overall negative charge  one material ends up with fewer electrons, so it now has an overall positive charge.
  • 13. 13 of 5 © Boardworks Ltd 2011 All materials are made of atoms, which contain electric charges. An atom has equal numbers of electrons and protons and so has no overall charge. Around the outside of an atom are electrons, which have a negative charge. The nucleus at the centre of an atom contains protons, which have a positive charge. Electrons do not always stay attached to atoms and can sometimes be removed by rubbing. Where does static charge come from?
  • 14.
  • 15. 15 of 38 © Boardworks Ltd 2007 Static electricity has many uses, including: How can static electricity be used?  photocopiers and laser printers  filtering factory smoke  spray painting cars  heart defibrillators
  • 17. 17 of 36 © Boardworks Ltd 2010 What is electric charge? Electric charge is a feature of certain elementary particles, such as electrons and protons, that causes them to interact with each other. The unit of electric charge is the coulomb, C. One coulomb is equivalent to the charge transported by 1 ampere of current in 1 second.  Protons have an electric charge of 1.60 × 10-19 C (e).  Electrons have an electric charge of -1.60 × 10-19 C (-e). Like charges repel; unlike charges attract.
  • 18. 18 of 36 © Boardworks Ltd 2010 Charges and electric fields All charged objects are surrounded by a region called an electric field. An electric field is a region where a charged particle will experience a force. Electric fields can be represented by electric field lines. ● The direction of the lines represents the direction of the field – it shows the direction a positive charge would move in the field. ● The distance between lines represents the strength of the field – the closer the lines, the stronger the field.
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  • 21. 21 of 36 © Boardworks Ltd 2010 Charged particle interactions
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  • 26. 26 of 36 © Boardworks Ltd 2010 Coulomb’s experiments In 1783, the French physicist Charles Augustin de Coulomb measured the electrostatic force between two electric charges. He deduced that the magnitude of the force, F, between charges Q1 and Q2 is:  proportional to the product of Q1 and Q2 (i.e. Q1 × Q2)  inversely proportional to the square of the distance (r) between them. This forms the basis of Coulomb’s law.
  • 27. 27 of 36 © Boardworks Ltd 2010 Coulomb deduced that: where k is a constant of proportionality: Coulomb’s law εo is the permittivity of free space: 8.85 × 10-12 C2 N-1 m-2 (or 8.85 × 10-12 Fm-1) 4πεo 1 Q1Q2 r2 F = 4πεor2 Q1Q2 F = or or: 4πεo 1 k = r2 Q1Q2 F  r2 kQ1Q2 F = So Coulomb’s law can be stated as:
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  • 29. 29 of 36 © Boardworks Ltd 2010 Coulomb’s law: true or false?
  • 30. 30 of 36 © Boardworks Ltd 2010 ELECTRIC FIELD STRENGTH Electricity and Magnetism
  • 31. 31 of 36 © Boardworks Ltd 2010 Placing a charge in an electric field
  • 32. 32 of 36 © Boardworks Ltd 2010 Electric field strength Electric field strength is defined as the force experienced per unit charge. The charge in the equation refers to the charge of the particle in the field. electric field strength = force / charge E = F / Q Example: What is the electric field strength around a point charge if a 3.20 × 10-19 C charge experiences a force of 7.30 × 10-15 N? E = (7.30 × 10-15 ) / (3.20 × 10-19 ) E = 2.28 × 104 NC-1 E = F / Q
  • 33. 33 of 36 © Boardworks Ltd 2010 Electric field strength: uniform fields The electric field between two parallel plates (e.g. capacitor plates) is uniform: a charge will experience the same force wherever it is placed between the plates. The electric field strength depends on two factors: the voltage between the plates and the distance between them. electric field strength = voltage / distance E = V / d The units of E in this instance are volts per metre (Vm-1).
  • 34. 34 of 36 © Boardworks Ltd 2010 Electric field strength: radial fields
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  • 36. Electric field strength vs distance for a sphere For the case of sphere of radius a.
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  • 38. 38 of 36 © Boardworks Ltd 2010 Zero values of E between two charges (1) In the case of two positive or two negative point charges, there is a point along the line between the two charges where the electric field strength is zero. Can you explain why? E is a vector quantity that acts in the same direction as the force on a positive charge placed in the field. Therefore the strength of each field will be equal and opposite at some point along the line above, and the vector sum will be zero. Where will that point be in the above example if Q1 = 2Q2?
  • 39. 39 of 36 © Boardworks Ltd 2010 Zero values of E between two charges (2) When E is 0: E1 = E2 At what point will E be zero if Q1 = 2Q2? Substitute in equations for E: Q1/4πεor1 2 = Q2/4πεor2 2 Cancel constants: Q1/r1 2 = Q2/r2 2 Q1 = 2Q2 so: 2Q2/r1 2 = Q2/r2 2 Cancel Q2 values from each side: 2 = r1 2/r2 2 Square root each side: √2 = r1/r2 Multiply both sides by r2: r1 = r2√2
  • 40. 40 of 36 © Boardworks Ltd 2010 Zero values of E between two charges (3) r1 = r2√2 At what point will E be zero if Q1 = 2Q2? This means that the point lies along the line further from Q1 than from Q2. The exact distance can be calculated if necessary by working out the fraction of the total distance r1 and r2 make up:  r1 is √2/(1+√2) of the total distance from Q1  r2 is 1/(1+√2) of the total distance from Q2.
  • 41. 41 of 36 © Boardworks Ltd 2010 ELECTRIC POTENTIAL Electricity and Magnetism
  • 42. Electric potential vs potential difference
  • 43. 43 of 36 © Boardworks Ltd 2010 What is electric potential? If a positive test charge is moved from infinity to a position in an electric field, the electric potential energy (Ep) of that charge will change. In other words work is done on the charge. electric field Zero Ep can be set anywhere, but in electric fields around a point charge it is set at infinity. This is because the strength of the field would also be zero at infinity. positive test charge at infinity
  • 44. 44 of 36 © Boardworks Ltd 2010 What is electric potential? Rearranging gives: The electric potential at a certain position in an electric field is the work done per unit positive charge when a positive test charge is moved from infinity to that position. electric potential energy = electric potential × charge Ep = QV V = Ep / Q electric potential = electric potential energy / charge In other words, electric potential is voltage, and is measured in volts (V) or joules per coulomb (JC-1).
  • 45. Electric potential of point charge
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  • 47. 47 of 36 © Boardworks Ltd 2010 Electric potential and radial fields The electric potential, V, near a point charge, Q, at a distance r is given by the formula: 4πεor Q V = Example: What is the electric potential at a distance of 20.0mm around a point charge of 1.40 × 10-8 C? V = 6294V 4πεor Q V = 1.40 × 10-8 4 × π × (8.85 × 10-12) × 0.02 V =
  • 48. Electric potential due to multiple charges
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  • 51. Vector addition also applies for electric field strengths
  • 52. Relationship between Electric field and potential
  • 53. 53 of 36 © Boardworks Ltd 2010 Equipotentials
  • 54. 54 of 36 © Boardworks Ltd 2010 Potential gradients
  • 55. 55 of 36 © Boardworks Ltd 2010 Electric fields: equations summary
  • 57. Charged conducting sphere Inside a charged conducting sphere the electric field is zero due to equilibrium, the potential remains constant at the value it reaches at the surface Outside of the sphere the electric field environment is identical to that of a point charge. Therefore the potential is the same as that of a point charge:
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