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2.1.1 – 2 Electric Fields
An electric field is the region around a charged
object where a force is exerted on a charged
object.
Coulombs law states that the force exerted on a
pair of charged objects is proportional to the
product of their charges and inversely
proportional to the square of the distance of
separation. ie
F = kQ1Q2
r2
If we consider how one of the charged (Q1)
objects will affect any other charge brought
near it we need to consider the force it will
exert on just one coulomb of charge and then
scale it accordingly. Ie from coulombs law this
would be F/Q2
F = kQ1
Q2
r2
This is called the Electric Field Strength
E = F/q
Electric Field Strength E is the force exerted on a
unit charge (one coulomb) placed in an electric field
It’s units are NC-1, and it is a vector quantity like
gravitational field strength
We already know that the force exerted by charged
objects depends on the size of the charges and their
separation as well as the substance separating them,
therefore according to Coulombs law……
F =
1 . qQ
(4) r2
If 1 = k
F = kqQ
r2
(4)
Therefore if the charge we place in the field caused by Q is q
then since E = F/q it will experience a field strength of
E =
1 . Q
(4) r2
E = kQ
r2
The value of the Electric field strength will decrease as we
move further away from the charge producing the field
according to the inverse square law E  1/r2
Electric Field
Strength in
uniform fields
Circular motion of charged
particles in electric fields
When an atom such as hydrogen, causes
an electron to orbit around the outside,
it does so because of the electrostatic
force between the two charges. This
can happen in radial fields and uniform
fields as in the fine beam tube!
Therefore
1.1 * 10-8m
+
electrostatic force = centripetal force
kqQ
r2
And so v2 = kqQ
mr
= mv2
r
Putting in all the relevant
data gives us an orbital
speed of 1.6 * 106 ms-1
Uniform Electric Fields
As seen in the semolina &
olive oil demonstration we
know that the field
between two parallel
plates is uniform in the
central region.
In a uniform field the
field lines are parallel
and a constant distance
apart.
The electric field
strength varies very
little
Work done in an electric field
Whenever a force causes an object to move in the
direction of the force work is said to be done.
Therefore if an electric field exerts a force on a
charged object it must be doing work.
As we know
work done = force * distance moved in the direction
of the force
W = Fx
As we learned in Module 2 W = QV when a charge is
moved through a p.d. work is done and therefore
QV = Fx
We could therefore prove that the voltage V is
proportional to the distance moved x, since the
charge moving and the force depends on the the
charges and the distance from it.
So for a uniform field we end up with lines where the
potential of that point and all points along it are equal.
Just like contour lines on a map, joining points of equal
height, which is how we described potential in module 2
when talking about mountains.
Therefore the electric field also has contour lines or
equipotential lines where the same amount of work
would be done if you moved a unit charge to any point
on that line from a starting point.
However, no work is done (energy gained or lost) by
moving a charge along an equipotential line just like Ep
when moving around a mountain on a contour line!
Since E=F/Q
We get E = V/x measured in Volts/metre
Therefore the Electric Field Strength is
the potential gradient for the field.
If the electric field strength is large the
force exerted on the charged objects in the
field will also be large. Ie if you increase
the PD there will be a larger force
exerted
If you move the plates closer together the
potential gradient will be steeper and
therefore the Electric field strength so
greater forces will be exerted.
Electric Field Strength in
Radial Fields
•Around a point charge we have a
different field pattern known as a
radial field
• This diagram shows how lines of
equipotential exist similarly to
contour lines on a map –
• Same energy needed to move a
charged object to any point on the
line
• No energy needed to travel
around the line
+Q
A charge of 20nC will
produce an electric field
around it whose Electric
field strength will
decrease as you move
away from it as shown.
30cm 20cm 10cm
Check the calculations!
These values can be
seen to obey the
inverse square law
as shown in the
graph.
+
25
18kNC-1
20
15
10
4.5kNC-1
5
0
0
5
10
15
20
25
30
35
2kNC-1
The shape of electric fields depends on the charged
object(s) producing them. If we are talking about a
single point charge, the field is radial. If we think of
other objects they can be modelled on magnetic fields,
remembering the field lines run from positive to
negative!
Isolated charge Unlike charges
Like charges
What would the fields look like for the situations
above??
The field lines indicate the direction
of the force experienced by a
positive charge placed in the field.
If the charge was negative the field
lines would point inwards.
As you can visualise from the field lines –
they get further apart as you move out
from the centre – the electric field
strength decreases as you move away
from the charge
+Q
Electric Field
Strength
The decrease obeys the inverse square
law since E = kQ/r2
Or
E  1/r2
Separation