Physics Chapter Three - Electric Fields and Charges

Electrostatics
Electricity and Magnetism

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

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The other electricity
Where can electricity be found in this lab scene?

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?

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.

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!

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.

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.

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?

Static electricity has many uses, including:
How can static electricity be used?
 photocopiers
and laser
printers
 filtering
factory
smoke
 spray painting cars
 heart
defibrillators

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.

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.

Charged particle interactions

Interaction of charges continued

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.

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:

Coulomb’s law: true or false?

ELECTRIC FIELD STRENGTH

Placing a charge in an electric field

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

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).

Electric field strength: radial fields

Electric field strength vs distance for a
sphere
For the case of sphere of
radius a.

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?

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

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.

ELECTRIC POTENTIAL

Electric potential vs potential difference

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

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

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

Equipotentials

Potential gradients

Electric fields: equations summary

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:

Physics Chapter Three - Electric Fields and Charges

Physics Chapter Three - Electric Fields and Charges

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