**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**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**

V is the

d is the

**p.d. between**the platesd 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

Remember the

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

This is measured in

It is defined as

**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)**Fleming's Left-hand rule on conductors**

Fleming's left hand rule helps show the

A wire with a current in a magnetic field will experience a force (creating motion)

**motor rule**.A wire with a current in a magnetic field will experience a force (creating motion)

These give you the

*:*__direction of__**u**__Th__**b -**__m__**otion or**__m__**rust (Force)**__Th____irst finger -__**F**__ield (Flux Density)__**F****econd Finger -**__S__**urrent**__C__This follows the equation:

**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

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:

There is

The force

For

The particles will always travel in a

Therefore you get the following equation:

**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

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

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

and from the first field

This gives us the equation

__if the particle has a lower velocity (lower mass) then it will be bent less. This is all to separate the isotopes more.__*Magnetic fields and charged particles,*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

B2Q__mv__= rB2Q

and from the first field

B1__E__= vB1

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

The magnetic flux can be discovered with the equation:

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:

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

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

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

A

A

The ratio between turns and voltage can be shown as below (If transformer is 100% efficient)

**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__=__n____s__**Vp np**