Download Electric Fields

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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.
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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.
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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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Charged particle interactions
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Inverse-square law
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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.
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Coulomb’s law
Coulomb deduced
that:
Q 1Q 2
F
r2
or:
kQ1Q2 where k is a constant
F =
of proportionality:
r2
1
k =
4πεo
εo is the permittivity of free space:
8.85 × 10-12 C2 N-1 m-2 (or 8.85 × 10-12 F m-1)
So Coulomb’s law can be stated as:
1 Q 1Q 2
F =
4πεo r2
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or
Q 1Q 2
F =
4πεor2
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Coulomb’s law
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Effect of distance and charge on force
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Coulomb’s law: true or false?
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Placing a charge in an electric field
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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 = F/Q
E = (7.30 × 10-15 ) / (3.20 × 10-19 )
E = 2.28 × 104 N C-1
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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 (V m-1).
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Electric field strength: radial fields
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Electric field strength calculations
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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?
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Zero values of E between two charges (2)
At what point will E be
zero if Q1 = 2Q2?
When E is 0: E1 = E2
Substitute in equations for E: Q1/4πεor12 = Q2/4πεor22
Cancel constants: Q1/r12 = Q2/r22
Q1 = 2Q2 so: 2Q2/r12 = Q2/r22
Cancel Q2 values from each side: 2 = r12/r22
Square root each side: √2 = r1/r2
Multiply both sides by r2: r1 = r2√2
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Zero values of E between two charges (3)
At what point will E be
zero if Q1 = 2Q2?
r1 = r2√2
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.
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Electric field strength: summary
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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
positive
test charge
at infinity
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.
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What is electric potential?
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 = electric potential energy / charge
V = Ep / Q
In other words, electric potential is voltage, and is measured
in volts (V) or joules per coulomb (J C-1).
Rearranging gives:
electric potential energy = electric potential × charge
Ep = QV
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Electric potential and radial fields
The electric potential, V, near a point charge, Q, at a
distance r is given by the formula:
Q
V =
4πεor
Example: What is the electric potential at a distance of
20.0 mm around a point charge of 1.40 × 10-8 C?
Q
V =
4πεor
1.40 × 10-8
V =
4 × π × (8.85 × 10-12) × 0.02
V = 6294 V
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Electric potential calculations
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Equipotentials
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Potential gradients
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Electric potential: summary
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Gravitational fields vs. electric fields
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Glossary
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What’s the keyword?
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Electric fields: equations summary
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Multiple-choice quiz
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