Electric Fields exert forces on charged particles

Charged objects generate electric fields around them

A charged particle placed inside an electric field will experience a force due to the field

This force will cause the charged particle to accelerate (Newton’s 2nd Law)
Electric Field diagrams

We use lines of force to show the strength and direction of the force.

The closer the field lines the stronger the force.

The arrows point in the direction that a free positive test charge would move in the field.

The field lines are equally spaced between the parallel plates. This means the field strength is
constant. This is called a uniform field.
Work done, charge and potential difference

When the electric field exerts a force on the charged particle, the field does work on the charged
particle
o

i.e. energy is transferred from the electric field to the charged particle.
The potential difference between two points in an electric field is defined as the work done in
moving one coulomb of charge between the two points in the field.
V
W
Q
which is normally written as
W  QV
potential difference between two
points (V)
work done by field (J)
amount of charge moved (C)

From the above, we can see that a potential difference of 1 Volt means that 1 Joule of energy is
provided to 1 Coulomb of charge.
1 Volt = 1 Joule per Coulomb
1 V = 1 JC-1
Example
A positive charged particle of charge 30 C is released from point A.
The positive charge accelerates towards point B.
The potential difference between A and B is 20 kV
A
+
+
+
+
B
+
-
(a) Calculate the work done by the electric field on the charge.
(b) State the kinetic energy gained by the charge.
(a)
W=?
Q = 60 C = 60×10 C
V = 20 kV = 2000 V
-6
(b)
W  QV
W  3  0 106  2000
W  6  0 103 J
Work done by field = kinetic energy gained = 6×10-3 J
Using conservation of energy to calculate speed of charged particle
From the previous example, when the positive charge is released, then the electrical potential
energy stored by the field is converted to kinetic energy.
QV =
1 2
mv
2
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 = 9.11 × 10-31 kg, magnitude of charge on an electron = 1.6x10-19 C – these
values are provided in the data sheet)
(a)
Ek gained = W = QV = 1.6x10-19 × 200
= 3.2 × 10-17 J
(b)
Ek=
1 2
mv = 3.2 × 10-17
2
1
3  2 1017   9 1110 31  v 2
2
3  2 1016
v2 
1
 9 111031
2
v
3  2 1016
1
 9 111031
2
v = 84 × 106 m s-1
Magnetic Fields


When a charged particle moves, a magnetic field is generated around it, in addition to its electric
field.
o
A stationary charged particle generates an electric field
o
A moving charged particle generates an electric field and a magnetic field
The left-hand grip rule indicates the direction of the magnetic field according to the movement
of negatively charged particles, i.e. the direction of electron flow
direction of
electron flow
Direction of magnetic force exerted on a moving charge within a magnetic field

When a charged particle is inside a magnetic field, it experiences a force exerted by the magnetic
field.

The direction of the magnetic force is perpendicular to both the direction of the magnetic field,
and the direction that the charged particle is moving in.

The direction of the magnetic force and subsequent motion of the charged particle can be found
using the right hand motor rule.

The right-hand motor rule provides the direction of the magnetic force on a negatively charged
particle
o
The thumb points in the direction of motion (M)

i.e. direction of the magnetic force and the way that the magnetic force will
cause the particle to move.
o
The index finger gives the direction of the magnetic field (F)
o
The middle finger gives the direction of electron flow, or current (I)

For a positive charge moving in a magnetic field, the same rule is applied but the left hand is
used.
Examples
Confirm these directions using the right-hand motor rule or left-hand motor rule – convince yourself!
(a)
The magnetic force causes the electron to move out of the page towards you.
(b)
X indicates that the magnetic field direction is into the page.
The magnetic field causes the electron to curve to the left.
(c)
 indicates that magnetic field direction is out of the page.
The magnetic field causes the electron to curve upwards.
More on magnetic force

If the charged particle moves parallel to the magnetic field, then no force is exerted by the
magnetic field and the particle’s direction is unchanged.
o

The charged particle must “cut across” the magnetic field lines to experience a force and
resultant change in direction
A neutron will pass through a magnetic field with no change in direction since magnetic fields
only exert a force on a charged particle.
Particle accelerators

Particle accelerators use electric fields and magnetic fields to accelerate subatomic particles to
velocities close to the speed of light.

Particle accelerators are used to probe the structure of matter by breaking up subatomic
particles into the smallest possible components, called fundamental particles.
o
This is done by either causing the high-energy particle beam to collide with a stationary
target, or by causing two high-energy particle beams to collide together head-on

Particle accelerators also have many other areas, including important medical applications in
imaging and cancer treatment (radiotherapy)

There are three main types of particle accelerators:
o
linear accelerator (LINAC)
o
cyclotron
o
synchrotron
Linear accelerator (LINAC)

Charged particles, usually electrons or protons, are accelerated in a long, linear vacuum pipe
through a series of electrodes by an alternating voltage.

The beam of particles is then directed at a target.
o
LINACS make use of electric fields only
o
An old cathode ray TV tube and an oscilloscope are examples of low-energy LINACs
Cyclotron

Cyclotrons accelerate protons, or sometimes heavier ions like alpha particles.

Cyclotrons are used in hospitals to produce radioactive isotopes for medical imaging.

A cyclotron consists of two D-shaped, hollow metal structures called “dees”, placed in a vacuum.
The “dees” are surrounded by a ring of electromagnets. The diagram shows the cyclotron viewed
from above.
electromagnets

Protons are injected at a point near the centre.

The electric field between the “dees”, generated by a high-voltage alternating supply, accelerates
the protons

The magnetic field generated by the electromagnets causes the particles to move in a circular
path.

Every time the particle crosses from one dee to another it accelerates.

After each acceleration, the particle moves to a slightly larger orbit.

When it reaches the outer edge of the cyclotron the high-energy proton beam is extracted and
directed at a target.
Synchrotron

Synchrotrons were developed from LINAC and cyclotron technology

This is similar to a linear accelerator, bent into a ring so the charged particles can be
given more energy each time they go round.

Electromagnets keep the particles in a curved path. As the speed increases, the magnetic field
strength is increased.

As the charged particles are deflected round the ring, they emit high-energy electromagnetic
radiation which can be gathered and used in experiments.
For interest only – the Large Hadron Collider (LHC)
The Large Hadron Collider (LHC) at CERN is the world’s largest scientific instrument. It is located near
Geneva, where it spans the border between Switzerland and France. It is a particle accelerator used
by physicists to study the smallest known particles – the fundamental building blocks of all things.
At CERN, two beams of subatomic particles called ‘hadrons’ – either protons or lead ions – travel in
opposite directions inside a 27 km circular accelerator about 100 m underground, gaining energy
with every lap. The particles complete over 10,000 laps every second! By colliding the two beams
head-on at very high energies, physicists are able to create new particles and even recreate the
conditions that are believed to have occurred just after the Big Bang. Teams of physicists from
around the world then analyse the particles created in the collisions using special detectors.
It is difficult to get across the astonishing engineering achievement of the LHC. It is not only the
largest particle accelerator in the world; it is also the world’s largest freezer! It is the coldest and
emptiest place in the universe! In order to function properly it requires powerful superconducting
magnets that need be cooled to a temperature lower than outer space (only 1.9 degrees above
absolute 0 K, space is 2.7 K above absolute 0 K). Despite this, when the particles are collided they
create temperatures which are more than 100,000 times hotter than the sun. In order to analyse
more than 600 million proton collisions every second they have also had to create the world’s most
powerful supercomputing centre.