Electric Fields
Electricity & Electronics 1:
Electric Fields
AIM
It is likely that you covered some work on static electricity during your first two years in
secondary school. If you’ve forgotten all about it you’ll find some suggested reading to jog
your memory at the beginning of the unit.
The main work of this unit will introduce you to some of the theory of static electricity and
explain some applications, eg photocopying, pollution control and accurate spray painting.
OBJECTIVES
On completion this unity you should be able to:
• state that, in an electric field, a charge experiences a force.
• state that an electric field applied to a conductor causes the free electric charges in it
to move.
• state that when a charge Q is moved in an electric field, work W is done.
• state that the potential difference between two points is a measure of the work done
in moving one coulomb of charge between the two points.
• state that if one joule of work is done moving one coulomb of charge between two
points, the potential difference between the two points is one volt.
• state the relationship: V = W/Q .
• carry out calculations involving the above relationship.
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Electric Fields
Force Fields
In Physics, a field means a region where an object experiences a force without being touched.
For example, there is a gravitational field around the Earth. This attracts masses towards the
earth’s centre. Magnets cause magnetic fields and electric charges have electric fields around
them.
Electric Fields
In an electric field, a charged particle will experience a force. We use lines of force to show
the strength and direction of the force. The closer the field lines the stronger the force. Field
lines are continuous - they start on positive and finish on negative charge. The direction is
taken as the same as the force on a positive “test” charge placed in the field.
Electric Field Patterns
Positive point charge
+
Negative point charge
+ test charge
has a force
‘outwards’
+ test charge
has a force
‘inwards’
-
These are called radial fields. The lines are like the radii of a circle. The strength of the field
decreases as we move away from the charge.
Electric Field Patterns
Positive and negative point charges
-
Parallel charged plates
+
+
+
+
+
-
The field lines are equally spaced between the parallel plates. This means the field strength is
constant. This is called a uniform field.
Electric fields have certain similarities with gravitational fields.
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Electric Fields
Gravitational Fields
h
If a mass is lifted or dropped through a height then work is done i.e. energy is changed.
If the mass is dropped then the energy will change to kinetic energy.
If the mass is lifted then the energy will change to gravitational potential energy.
Change in gravitational potential energy = work done.
Electric Fields
Consider a negative charge moved through a distance in an electric field. If the charge moves
in the direction of the electric force, the energy will appear as kinetic energy. If a positive
charge is moved against the direction of the force as shown in the diagram, the energy will be
stored as electric potential energy.
Change in electric potential energy = work done
If the charge moved is one coulomb, then the work done is the potential difference or voltage.
If one joule of work is done in moving one coulomb of charge between two points in an
electric field, the potential difference, (p.d.) between the two points is one volt.
1 volt = 1 joule per coulomb
W = QV
In this section W will be used for the work done i.e. energy transferred.
Example:
A positive charge of 3 µC is moved, from A to B, between a potential difference of 10 V.
(a)
Calculate the electric potential energy gained.
(b)
If the charge is now released, state the energy change.
B
A
(c)
How much kinetic energy will be gained on reaching
+
the negative plate?
+
+Q
+
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(a)
W
= QV= 3 × 10 × 10
+
= 3 × 10-5 J
(b)
Electric potential energy to kinetic energy
(c)
By conservation of energy the energy will be the same, i.e. 3 × 10-5 J.
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Electric Fields
Moving Charges in Electric Fields
From the previous example, when the positive charge is released at plate B then the electrical
potential energy is converted to kinetic energy.
QV = ½mv2
Example
An electron is accelerated (from rest) through a potential difference of 200 V.
Calculate
(a)
the kinetic energy, Ek gained.
(b)
the final speed of the electron.
(Mass of an electron = 9.1 × 10-31 kg, charge on an electron = -1.6x10-19 C)
(a)
Ek =½mv2
= QV = 1.6x10-19 × 200
= 3.2 × 10-17 J
(b)
½mv2 = 3.2 × 10-17
3.2 × 10 − 17 × 2 3.2 × 10 − 17 × 2
v2 =
=
m
9.1 × 10 − 31
v = 8.4 × 106 m s-1
Applications of electric fields (for background interest)
A television involves the use of electron guns. The electrons gain kinetic energy by
accelerating through an electric field. Deflection of the electrons is usually done by
electromagnetic coils, although flat screen tubes are now dependent on electrostatic
deflection.
An oscilloscope also depends on electric fields acting on electrons.
+
E le c t r o n G u n
-
-
+
Electrostatic Spraying makes use of electric fields. Paint or powder particles are blown from a
nozzle, where they acquire a charge. The object to be coated is earthed. The charged paint or
powder particles follow the field lines and so reach the object, some reaching the back of the
object as well as the front.
Other applications include photocopiers, ink jet and laser printers.
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Electric Fields
Electric fields
1.
Draw the electric field pattern for the following charges:
+
(a)
2.
-
(b)
(c)
+
-
Describe the motion of the small test charges in each of the following fields.
(a)
(b)
+test charge
+test charge
+
(c)
+
+
+
+
-
-
-Q
(d)
+
+
+
+
-
+
Q
3.
An electron volt is a unit of energy. It represents the change in potential energy of an
electron which moves through a potential difference of 1 volt. If the charge on an
electron is 1.6x10-19 C, what is the equivalent energy in joules?
4.
Mass of an electron = 9.1 × 10-31 kg
Charge on an electron = 1.6 × 10-19 C
The electron shown opposite is accelerated
across a p.d. of 500 V.
(a)
How much electrical work is done?
(b)
How much kinetic energy has it gained?
(c)
What is its final speed?
5.
+
+
+
+
+500 V
-e
-
Electrons are ‘fired’ from an electron gun at a screen. The p.d. across the gun is
2000 V. After leaving the positive plate the electrons travel at a constant speed to the
screen. Assuming the apparatus is in a vacuum, at what speed will the electrons hit
the screen?
-
- e
+
+
+
+
E le c t r o n g u n
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Electric Fields
6.
7.
8.
What would be the increase in speed of an electron accelerated from rest by a p.d. of
400 V?
An x-ray tube is operated at 25 kV and draws a current of 3 mA.
(a)
Calculate
(i) the kinetic energy of each electron as it hits the target
(ii) the velocity of impact of the electron as it hits the target
(iii) the number of electrons hitting the target each second.
(mass of electron = 9.1 × 10-31 kg charge on electron = 1.6 × 10-19 C)
(b)
What happens to the kinetic energy of the electrons?
Sketch the paths which
(a) an a-particle,
(b) a b-particle,
and
(c) a neutron,
would follow if each particle entered the given electric fields with the same velocity.
(Students only studying this unit should ask for information on these particles).
P a t h o f p a r t ic le
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P a t h o f p a r t ic le
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Electricity and Electronics