Electric Fields
An electric field is created by an electric charge. Not only is it caused by an electric field, it exerts an electrical force on any charged object in a field.
Electric Field Strength - Unit Force per Unit Charge
E = F
Q
Q is positive charge
Electric Field Strength - Unit Force per Unit Charge
E = F
Q
Q is positive charge
Field Patterns
Point Charge
Plate Charges
The field lines are equally spaced and parallel
Coulomb's Law
Coulomb's Law states that the field strength between two charges is proportional to the sum of the charges and inversely proportional to the squared distance between them.
This gives the equation:
This gives the equation:
You can work out the electric field strength for a point charge using the equation below.
r is the distance you are from the centre of the field
Potential Gradient
The potential gradient is the electric field strength between two charged plates
E = V
d
d
V is the p.d. between the plates
d is the distance between the plates (not the length)
d is the distance between the plates (not the length)
Charged particle in a field
A charged particle can be fired into the electric field at any angle.
When it does this it will be attracted towards one the plates depending on its charge (opposites attract)
Remember the only force acting is the one towards the plates.
Between the plates, the particle will gain kinetic energy - Note: it will stop gaining kinetic energy when it leaves the field.
When it does this it will be attracted towards one the plates depending on its charge (opposites attract)
Remember the only force acting is the one towards the plates.
Between the plates, the particle will gain kinetic energy - Note: it will stop gaining kinetic energy when it leaves the field.
Magnetic Fields
Magnetic fields are areas where charged particles, conductors and magnets can experience a force.
Magnetic flux (The field lines) travel from north to south
Magnetic flux (The field lines) travel from north to south
Magnetic Flux Density
The strength of a field is measured by its magnetic flux density (density of field lines)
This is measured in Teslas and given the symbol B
It is defined as Unit force per unit current of unit length (seen in equation lower)
This is measured in Teslas and given the symbol B
It is defined as Unit force per unit current of unit length (seen in equation lower)
Fleming's Left-hand rule on conductors
Fleming's left hand rule helps show the motor rule.
A wire with a current in a magnetic field will experience a force (creating motion)
A wire with a current in a magnetic field will experience a force (creating motion)
These give you the direction of:
Thumb - motion or Thrust (Force)
First finger - Field (Flux Density)
Second Finger - Current
Thumb - motion or Thrust (Force)
First finger - Field (Flux Density)
Second Finger - Current
This follows the equation:
F = BILsinθ
F = BILsinθ
F is the force acting on the wire (N)
B is the magnetic flux density (T)
I is the (conventional) current (A)
L is the length of the wire in the field (m)
sinθ is for when the wire isn't going through perpendicular to the direction of flux density
B is the magnetic flux density (T)
I is the (conventional) current (A)
L is the length of the wire in the field (m)
sinθ is for when the wire isn't going through perpendicular to the direction of flux density
The force experienced is due to two magnetic fields interfering.
The wire creates a magnetic field. This interferes with the external magnetic field. There is a lower magnetic flux density above which means the wire will move towards it.
The wire creates a magnetic field. This interferes with the external magnetic field. There is a lower magnetic flux density above which means the wire will move towards it.
... on charged particles
The same thing happens to a charged particle (positive or negative) in a magnetic field. It follows a similar equation but with a few tweeks:
F = BQv
There is no force acting on the particle when it is stationary
The force always acts perpendicular to direction of motion
For electrons the current is going in the opposite direction to the direction of motion (it is conventional current)
The particles will always travel in a circular path
Therefore you get the following equation:
mv^2 = BQv
r
mv = BQ
r
F = BQv
There is no force acting on the particle when it is stationary
The force always acts perpendicular to direction of motion
For electrons the current is going in the opposite direction to the direction of motion (it is conventional current)
The particles will always travel in a circular path
Therefore you get the following equation:
mv^2 = BQv
r
mv = BQ
r
This is used in Mass Spectrometry (Look at Chemistry for more on mass spectrometry)
Mass Spectrometer
A Mass spectrometer determines the abundance of isotopes of an element.
First the atoms are ionised.
They then get accelerated through two electric plates in a magnetic field.
They then enter a large magnetic field and are turned towards a detector.
First the atoms are ionised.
They then get accelerated through two electric plates in a magnetic field.
They then enter a large magnetic field and are turned towards a detector.
Accelerating
Ions are accelerated through a potential difference. Those with larger mass have a lower velocity and vice versa.
This means the isotopes can be separated in the next processes.
This means the isotopes can be separated in the next processes.
Electric and Magnetic fields
When a particle enters an electric field it is pulled towards one of the plate. When a magnetic field is put over the top it too exerts a force on the particle. In a mass spectrometer they work together so only ions with the a certain velocity get through (separating the differently massed ions).
For an ion to pass through undeterred then the forces from the electric and magnetic field need to balance.
EQ = BQv
For an ion to pass through undeterred then the forces from the electric and magnetic field need to balance.
EQ = BQv
Ions in Magnetic Field
As shown in Magnetic fields and charged particles, if the particle has a lower velocity (lower mass) then it will be bent less. This is all to separate the isotopes more.
From all this we can determine the radius of the particle once it has gone through a mass spectrometer
we have from the second field
mv = r
B2Q
and from the first field
E = v
B1
This gives us the equation
mE = r
B1B2Q
From all this we can determine the radius of the particle once it has gone through a mass spectrometer
we have from the second field
mv = r
B2Q
and from the first field
E = v
B1
This gives us the equation
mE = r
B1B2Q
Magnetic Flux
Magnetic Flux is the the field lines flowing between north and south.
It is measured in Weber's (Wb)
The magnetic flux can be discovered with the equation:
ϕ = BAcosθ
It is measured in Weber's (Wb)
The magnetic flux can be discovered with the equation:
ϕ = BAcosθ
It is defined as the magnetic flux density multiplied by the perpendicular cross-sectional area of the wire
Magnetic Flux Linkage
When coils pass though the magnetic flux then more than one turn is the same amount of magnetic flux so to work out the magnetic flux linkage you get:
ϕL = BAn
When n is the number of turns in the coil
ϕL = BAn
When n is the number of turns in the coil
Electromagnetic Induction
A changing magnetic flux density induces an electromotive force (e.m.f)
If a conductor moves through a magnetic field then an e.m.f will be produced producing a current itself
This follows Fleming's Right-hand Rule. Same as Fleming's Left hand rule but on the right hand instead
If a conductor moves through a magnetic field then an e.m.f will be produced producing a current itself
This follows Fleming's Right-hand Rule. Same as Fleming's Left hand rule but on the right hand instead
Faraday/Lenz's Law
Faraday noticed that when a wire moves through magnetic flux density the magnetic flux linkage remains the same but there is no current. But when it rotates or enters a field then an e.m.f is induced. This lead to the conclusion that the e.m.f is the same as the rate of change of magnetic flux linkage.
Lenz then noted that because the induced current creates its own field in the opposite direction that in fact the e.m.f works in the opposite direction. Putting the minus on the equation
Induced e.m.f = - rate of change of magnetic flux linkage
Lenz then noted that because the induced current creates its own field in the opposite direction that in fact the e.m.f works in the opposite direction. Putting the minus on the equation
Induced e.m.f = - rate of change of magnetic flux linkage
If you enter a coil perpendicular to the direction of magnetic flux but don't rotate it when it's inside the magnetic flux linkage remains constant and so you get a graph like below where e.m.f rises as the coil enters and flux increases but isn't induced once the coil is fully in.
When a coil rotates in a field then an e.m.f is produces an a.c. current 90 degrees out of sync with the e.m.f. You may need to know this graph.
The alternating magnetic flux induces an e.m.f in the other coil.
A step-up transformer has more coils on the secondary coil and so induces a larger voltage
A step-down transformer has fewer coils on the secondary coil and so induces a smaller voltage.
The ratio between turns and voltage can be shown as below (If transformer is 100% efficient)
Vs = ns
Vp np
A step-up transformer has more coils on the secondary coil and so induces a larger voltage
A step-down transformer has fewer coils on the secondary coil and so induces a smaller voltage.
The ratio between turns and voltage can be shown as below (If transformer is 100% efficient)
Vs = ns
Vp np