Download Electric Fields

Advanced Higher Physics
Unit 2
Electric Fields
Size of charged particles
Powers of ten video
Static Electricity
What do these things have in common?





Crackles when combing hair.
Cling film sticking to your hands.
Clothes clinging to each other
in a dryer.
Getting a shock when rubbing
your feet on a carpet.
Lightning.
They are all caused by static electricity.
Static electricity is due to electric charge that builds up on the
surface of an insulator.
The charge that has built up cannot easily flow away from the
insulator, which is why it is called static electricity.
Where does static charge come from?
electron
(negative
charge)
All materials are made of
atoms, which contain electric
charges.
proton
(positive
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.
An atom has equal amounts of negative and positive charges which
cancel each other out. This means an atom has no overall charge.
Electrons do not always stay attached to atoms and can sometimes be
removed by rubbing.
Where does static charge come from?
Static charge can build up when two
materials are rubbed together, such as
a plastic comb moving through hair.
When this happens electrons are
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.
Creating static charge
An insulating material can be charged by friction.
For example, if an insulator is rubbed with a cloth, it can become
charged in one of two ways:
A. Electrons move from
the cloth to the insulator.
B. Electrons move from
the insulator to the cloth.
Charging a polythene rod
Charging a polythene rod
If an insulator made of polythene is rubbed with a cloth,
electrons move from the cloth to the insulator.
What charge does the cloth now have?
The cloth is positively charged.
What charge does the polythene insulator now have?
The insulator is negatively charged.
Charging an acetate rod
Charging an acetate rod
If an insulator made of acetate is rubbed with a cloth,
electrons move from the insulator to the cloth.
What charge does the cloth now have?
The cloth is negatively charged.
What charge does the polythene insulator now have?
The insulator is positively charged.
Static charge
Identifying unknown charge
If a rod has an unknown charge, how can the unknown charge be
identified using a positively charged rod?
?
 If the unknown charge is brought near to a positively charged
rod and it is attracted to this rod, then the unknown charge
negative
must be ________.
 If the unknown charge is brought near to a positively charged
rod and it is repelled by this rod, then the unknown charge must
positive
be ________.
Identifying unknown charge
If a rod has an unknown charge, how can the unknown charge be
identified using a negatively charged rod?
?
 If the unknown charge is brought near to a negatively charged
rod and it is attracted to this rod, then the unknown charge
positive
must be ________.
 If the unknown charge is brought near to a negatively charged
rod and it is repelled by this rod, then the unknown charge must
negative
be ________.
Inducing a temporary charge
If a negatively charged rod is brought near to a piece of
paper, the paper sticks to the rod.
The paper is uncharged (equal amounts of + and -), so why does
it stick to the rod?
+-+-++-+-+-
+-+-+As the negatively charged rod approaches the paper,
the electrons in the paper are repelled away from the rod.
This makes one side of the paper positive and one side negative. A
charge has been induced on the paper and the positive side of the
paper is attracted to the negative rod.
Inducing a temporary charge
If a negatively charged rod is brought near to a piece of
paper, the paper sticks to the rod.
The paper is uncharged (equal amounts of + and -), so why does
it stick to the rod?
+-+-++-+-++-+-+-
As the negatively charged rod approaches the paper,
the electrons in the paper are repelled away from the rod.
This makes one side of the paper positive and one side negative. A
charge has been induced on the paper and the positive side of the
paper is attracted to the negative rod.
Uses of static electricity
Static electricity can be dangerous but it
can also be useful, as long as it is used
carefully.
Examples of uses of static electricity are:
Photocopiers
1. ___________________
Printers
2. ___________________
Spray painting
3. ___________________
Pollutant removers
4. ___________________
How a photocopier works
Electrostatic paint spray
Static electricity can be used to spray a car with paint:
+
-Paint gun nozzle has
Car is
a positive
negatively
charge.
charged.
electrostatic generator
The nozzle of the paint gun is
connected to one terminal of an
electrostatic generator.
The other terminal is
connected to the metal
panel, which is earthed.
Electrostatic paint spray
The spray gun is designed to produce tiny charged droplets of paint.
+
+ + +
+Paint gun nozzle has
Car is
a positive
negatively
charge.
charged.
electrostatic generator
As a result the charged droplets are attracted to the car body
panel. This gives a uniform coating of paint.
Also, the droplets travel along the lines of force of the
electrostatic field to reach hidden parts of the panel.
Danger of static electricity
Filling fuel, rollers for paper
and grain shoots are situations
where charge can be a problem.
Static can build up as the fuel flows along the pipe or paper rolls
over rollers or grain shoots out of tubes.
This can easily lead to a spark and then an explosion.
To prevent this happening, the nozzles or rollers are made out of
metal so any charge build up is conducted away.
Large petrol tankers always have earthing straps between the tanker
and the storage tank to prevent the risk of sparks.
The Gold Leaf Electroscope
An electroscope can be used to
detect the presence and type of
charge on both metallic and non
metallic objects.
Charging an electroscope
Charging an electroscope
1. Bring up a negative charge close to electroscope
Polythene rod
Charging an electroscope
2. Earth cap with finger.
Polythene rod
Charging an electroscope
3. Remove finger.
Polythene rod
Charging an electroscope
3. Remove rod.
Polythene rod
The electroscope has become positively charged.
Charging an electroscope
1. Bring up a positive charge close to electroscope
Acetate rod
Charging an electroscope
2. Earth cap with finger
Acetate rod
Charging an electroscope
3. Remove rod
Acetate rod
The electroscope has become negatively charged.
Charging two identical sphere
with equal and opposite charges
1. Two initially uncharged metal spheres are touching.
Charging two identical sphere
with equal and opposite charges
2. A positively charged rod is brought closed.
Charging two identical sphere
with equal and opposite charges
3. Spheres are separated.
Charging two identical sphere
with equal and opposite charges
4. Charged rod is removed.
The two spheres have equal
and opposite charges.
Testing the sign of a charge
An electroscope is charged. For example
positively.
Testing the sign of a charge
A plastic object is rubbed and brought near
electroscope.
Testing the sign of a charge
If leaf rises further, the object is charged positively.
Testing the sign of a charge
If leaf goes down, the object is charged negatively.
Faraday’s Ice-Pail Experiment
1. A positively charged
sphere is suspended in
the can without
touching the walls of
the base.
2. The leaf rises.
3. Charged sphere
touches the can.
4. Sphere becomes
neutral but the can
stays positively
charged.
Coulomb’s law
Two points charges separated by a distance r exert a force on
each other- this force is called electrostatic.
Q1
Q2
r
This electrostatic force is:
•Proportional to the size of charges Q1 and Q2.
•Inversely proportional to the square of the distance r.
Q1Q2
F k 2
r
With k defined as:
1
40
where
 0  8.85 1012 Fm1
and is called the permittivity of free space
Therefore Coulomb’s Law is:
Q1Q2
F
40 r 2
If is positive then it is a repelling force.
If F is negative it is an attractive force.
In data
booklet.
Example
Calculate the force on each of the 2 charges shown:
+20µC
-25µC
•Ignore sign of charge
•Calculate magnitude of force first.
•Work on direction of forces depending on sign of charge
•Final answer should include magnitude and direction.
Electric Field
A positive charge exerts a positive (outwards) field.
A negative charge exerts a negative (inwards) field.
Two like charges
Two unlike charges
Parallel Plates
Electric Field Strength
The electric field strength is the force per coulomb which a
charged particle experiences.
Q1 generates an electric field E and Q2 experiences a force F.
Q1
F
E
Q1
Q2
Q1Q2

40 r 2Q1
E
r
In data
booklet
E
Q
40 r
Q1
40 r 2
With E, Electric Field Strength in NCˉ¹.
2
Example
Three charges are arranged in a line as shown.
Find the electric field at point P.
•Ignore sign of charge
•Calculate the electric field contribution from each charge
•Work on direction of forces depending on sign of charge
•Find total E by using signs
•Final answer should include magnitude and direction.
Electric fields and hollow conductors
The electric field inside a conductor is zero.
E=0
The electric field is perpendicular to the surface at all points
outside the conductor.
E=0
Inside: E=0
Outside:
E
E 1
r
2
r
Faraday’s cage video
Potential
The electric potential V at a point is the work done in bringing a
unit positive charge (1C) from infinity to that point.
W
V
Q
So 1 V is 1 JCˉ¹
For example work is done moving test charge Qt from a to b.
Qt
b
a
Potential Difference
The potential difference V between A and B is the work done in
moving a unit positive charge from A to B.
B
A
For a uniform field only:
work done = force x distance
QV  (QE )  d
V  Ed
V  Ed
In data booklet
Therefore Electric field strength can also be measured in Vmˉ¹.
Potential due to point charges
For a non uniform field, E is a measure of potential gradient.
dV
E
dx
also
E
dV  Edx
dV 
V
Q
40 x
r
dV



0

2
dx
Q
40 x
dx
2
Q
40 r 2
V
Q
r
1
0 dV  40  x 2 dx
V 
V
0
r
Q  1




40  x  
Q  1 
V 0 
   0
40  r

V 
Q
40 r
You do not need to
derive this!
Moving a positive charge from infinity requires work to be done
against the electric field, so the charge gains electrical potential
energy.
We define V to be zero at infinity.
V at all point closer must be positive.
Therefore:
V
Q
40 r
In data booklet
Notes:
•Potential is a scalar quantity.
•Potential due to several charges is the total of individual
potentials.
•Positive charges generate positive potentials.
•Negative charges generate negative potentials.
Example
A +40µC charge is placed next to a -40µC charge as shown.
0.60 m
0.80 m
R
Determine the electrostatic potential at P and R.
Potential around a hollow conductor
E=0
Outside
V 1
Inside V=
r
as
V
Q
40 r
value at the edge of the conductor.
This is because E=0 so no work is required to move
a charge around inside the conductor.
Inside: V
Outside:
V
V 1
r
r
Motion in an Electric Field
If a particle moves against the electric field
it gains potential electrical energy.
E p  QV
If a particle moves through the electric
field, its potential electrical energy is
transformed into kinetic energy.
1 2
mv  QV
2
B
2QV
v
m
Not in data
booklet
A
If v is 10% of c then relativistic effects need to be induced.
Example
The electric field strength between two plates is 3.6 kVmˉ¹ and
the plates separation is 25 mm.
Calculate the velocity of an electron when it reaches the opposite plate.
Entering an electric field
A charged particle entering an
electric field perpendicular to
the field acts like a projectile
in a gravitational field.
Horizontally: no force is acting
on the charged particle, so it
moves with a constant velocity
perpendicular to the field.
Vertically: there is an acceleration parallel to the field.
The acceleration is found using:
F qE
a 
m m
Example
An electron leaves the gun of an oscilloscope. It enters a plate with
a velocity of 9.5  10 6 ms 1 . The p.d. across the plates is 55V.
Calculate the velocity of the electron as it leaves the plates.
State if the velocity of the electron changes after leaving the plates.
Measurements
By measuring the deflection of an electron beam, find the velocity
of an electron as it leaves the parallel plates.
Distance of closest approach
A small positive charge Q1 moving from a large distance
towards a larger positive charge Q2.
The initial distance is considered to be infinite.
carbon nucleus
r
Ep  0
1 2
Ek  mv
2
Q1Q2
Ep 
40 r
Ek  0
At distance r, the kinetic energy has been converted into potential
energy and so the charge stops moving. This is called the distance of
closest approach.
change in kinetic energy = change in potential energy
1 2 Q1Q2
mv 
2
40 r
Q1Q2
r
2
20 mv
Not in data booklet
Example
1
A proton is travelling at 5.0  10 ms towards a carbon nucleus.
6
Find the distance of closest approach.
Millikan’s oil drop experiment.
Millikan determined the size of the charge of an electron.
He showed that there was a smallest ‘unit’ of charge or that charge
is ‘quantised’.
He did this by measuring the charge on numerous microscopic
charged oil drops.
All the charges were found to come in multiples of the basic ‘unit’:
2e, 3e or Ne where N is any whole number.
19
The charge of the electron e  1.6 10 C is the smallest amount
of charge detected.
Apparatus
+V
F=QE

QV
as V  Ed
d
F=mg
0V
When the oil droplet is stationary:
QV
 mg
d
mgd
Q
V
As m, g and d are constant; Q is proportional to 1/V.
Measurements
V
(V)
1/V
(Vˉ¹)
1/V
0.53
Q
( 1019 C )