Electric Fields

Electric Fields

 

Any object with a charge has an electric field around it- the region where it can attract or repel other charges.

 

1. Electric charge, Q, is measured in Coulomb's (C) and can be either positive or negative
2. Oppositely charged objects attract each other and like charges repel.
3. If a charged object is placed in an electric field then it will experience a force.

Coulomb's Law

You'll need Coulomb's law to work out F- the force of attraction or repulsion between two point charges.

 

Coulomb's law:

 

 

Q1= a charge

Q2= a charge

 

So the top one shows an attractive force and the force is towards the centre and F will be negative since -q-(+q) =-F

 

The bottom one shows a repulsive force where the force is directed outwards and F will be positive since -q-(-q)=+F

 

1. The force on Q1 is always equal and opposite to the force on Q2
2. It's an inverse square law. The further apart the charges are, the weaker the force between them
3. The size of the force, F, also depends of the permittivity of the material between the two charges.

Electric Field Strength

Electric field strength, E, is defined as the force per unit positive charge- the force that +1C would experience if it was placed in an electric field.

1. E is a vector pointing in the direction that a positive charge would move
2. The units of E are newtons per coulomb (N/C)
3. Field strength depends on where you are in the field
4. A point charge- or any body that behaves as if all is charge is concentrated at the centre has a radial field.

Radial Fields

1. E is the force per unit charge that a small, positive test charge, q, would feel at different points in the field. In a radial field, E, depends of the distance, r, from the point charge Q...
2. It's another inverse square law, E is proportional to r^2

 

This is what you use for finding the electric field strength of a point charge.

 

1. Field strength decreases as you go further away from Q

On the Y axis you have E, and on the X axis you have r. As r increases E decreases- inverse square law!

 

Electric Potential Energy

A charge in an Electric field has electric potential energy. Electric potential energy is the work that would need to be done in order to move a small charge, q, from infinity to a distance r away from a point charge Q...

U is another notation for E. This equation tells us the electric potential energy to move q from infinity to a distance r away from Q.

 

1. Infinity is used as if q were an infinite distance away from Q, the charged particle q would have zero potential energy.
2. In a repulsive force field (Q and q are both positive) you would have to do work against the repulsion to bring q closer to Q. The charge q gains potential energy as r decreases.
3. In an attractive field (Q is negative and q is positive) the charge q gains potential energy as r increases.

Electric Potential

Electric potential, V, is electric potential energy per unit positive charge...

This is the equation for electric potential. The difference between electric potential energy and electric potential is that one equation involves two q's the other only has one since it with electric potential, the q's cancel as it is per unit positive charge.

 

1. It is measure in Volts (V)
2. As with E, V is positive when the force is repulsive and negative when the force is attractive.

Uniform fields

A uniform field can be produced by connecting two parallel plates to the opposite poles of a battery.

1.  Field strength, E, is the same at all points between two plates and is...

1. V is the potential difference between the plates d is the distance between them
2. E can be measured in volts per metre
    

Faraday's and Lenz's Law

Faraday's and Lenz's Law

 

Lenz's Law

Lenz's law says: The induced emf is always in such a direction as to oppose the change that caused it.

 

This is saying that the emf will produce a force that opposes the motion of the conductor- in other words resistance.

 

Using Fleming's left hand rule point your thumb in the direction of the force of resistance- which is in the opposite direction to the motion of the conductor. (pretend the conductor is moving down, your thumb would be up)

 

Your second finger will now give you the direction of the induced emf.

 

If the conductor is connected as part of a circuit, a current will be induced in the same direction as the induced emf.

 

 

Faraday's Law

Faraday's Law

 

For a conductor moving in a magnetic field, the factors that affect the induced emf are:

• how quickly the magnetic field is changing
• the number of turns or loops of conductor in the field

This leads to Faraday's Law which states:

 

The induced e.m.f. is directly proportional to the rate of change of flux linkage (or rate of flux cutting)

 

A plane of wingspan 30m flies through a vertical field of strength 5 x 10^-4T. Calculate the emf induced across wing tips if its velocity = 150ms^-1.

Answer:
Calculate the area swept out each second by the wings. Multiply that by the field strength, B and you have got the flux swept out in a second.

 

So each second, 2.25Wb of flux is swept out.

 

This method leads us to a simpler equation for the emf induced by flux cutting:

E = Blv

Where:
B = magnetic flux density, T
l = length of the conductor cutting the field, m
v = speed at which the conductor cuts the field, m/s

Remember:it is only the motion perpendicular to the field that induces an emf.

 

 

Electromagnetic Induction

Electromagnetic Induction

 

So magnetic field lines are also known as flux and field strength is how close the field lines are together. The closer the lines the stronger the field. Magnetic field strength is also known as flux density.

 

Magnetic flux is the amount of field lines per area and is measured in Wb/m^2 (Tesla)

 

Magnetic flux density is the amount of field lines and is measured in Webers (Wb)

 

When you move a conductor (a metal wire is a conductor) inside a magnetic field, you create and e.m.f.

 

e.m.f is known as electromotive force. Its definition is:

 

A difference in potential that tends to give rise to an electric current.

 

Voltage is also known as potential difference and the difference between voltage and e.m.f is that when a circuit is open there is a maximum potential difference, when a circuit is closed a current flows round the circuit which gives rise to internal resistance and resistance across the load. When the circuit is closed there is a voltage drop.

 

If you swipe a metal bar through a magnetic field the movement creates an emf across the bar ends. This happens because as you swipe the bar through the field the electrons in the bar will experience a force and accumulate at the ends of the bar. One end will be positively charged and the other will be negatively charged. You then are creating a potential difference between the bar, an emf.

 

Any of the following would induce more emf:

• A longer bar would sweep more area of field
• A stronger field would mean that you swept through more lines of field in the same distance
• A faster sweep would mean you swept out more field per second

 

If you have a coil of wire and you move the coil inside a magnetic field you also create an e.m.f. and the amount of e.m.f. induced depends of the amount of flux passing through the coil and the number of turns on the coil. The product of these is called flux linkage.

 

What is the flux linkage in a coil of 15 turns and area of 25cm^2 in a field strength of 5T?

 

Answer:

 

Flux=Flux density x Area

 

Flux Linkage= Flux x number of coils

 

You need to work out the flux

 

So 5 x 25x10^-4 (you need it in metres not cm)  then multiply this by amount of turns...

 

5 x (25x10^-4) x 15= 0.1875Wb

 

Magnetic Field Questions

Magnetic Field Questions

 

Q1) Describe why a current-carrying wire at right angles to an external magnetic field will experience a force?

 

Q2) Write down the equation you would use to find the force on a current-carrying wire.

 

Q3) A square loop of wire carrying a current of 3A is within a magnetic field of strength 2x10^5T. Each side is 4cm long. Side A is at right angles to the magnetic field. Side B runs parallel to the magnetic field.

 

a)What is the force on side B of the loop.

 

b) Calculate the magnitude of the force on side A of the loop.

 

 

Answers are coming soon....

Magnetic Fields and Motors!

Magnetic Fields and Motors!

What is a magnetic field?

You can't see a magnetic field, you can only prove its existence by its affect on other objects. It only affects objects that have the ability to be magnetised (magnetic material). Magnetic fields tend to pull or push objects so a force is exerted. The definition is:

 

A magnetic field is a region where a force is exerted on magnetic material.

 

Magnetic fields can be represented by field lines. Field lines go from north to south. The strength of the magnetic field (B, measured in Tesla) is represented by how tightly packed the lines are- the closer the field lines, the stronger the field- just like contour lines on a map!

 

• Magnetic field lines = flux measures in Tesla (B)
• Magnetic field strength =flux density measured in Webers (Wb)
   

Field Lines

 

So this picture shows different field strengths of attractive, repulsive and neutral forces.

(a) Shows a typical magnet and the direction of force runs from north to south! The spacing between the lines is the magnetic field strength (B, Tesla). Closer=stronger.

 

(b) Shows an attractive force as unlike poles attract. Again the force goes from north to south. Notice that in the centre where the magnetic field is at its strongest, the lines of force (flux) are equally spaced. This indicates a uniform field. The field strength remains constant for any part of north to south in the middle. The field strength gets weaker with distance away from the attraction!

 

(c) Here is where two magnets are repelling each other. See there is no flux (field lines) in the centre? This is because the flux has cancelled out. You can imagine that if there were lines in the middle, the flux would overlap- when they do they cancel. So, in theory they never overlap. But the field strength is zero as there is no flux so there is no field strength.

 

There is a Magnetic Field around a wire carrying Electric Current

So for anything carrying a current, there is a magnetic field around it. No current and the magnetic field disappears. It looks like this:

 

 

Left image:

The electric current if flowing towards you (the picture has a tiny cross in the middle to tell you it is flowing towards you) then the magnetic field goes counter clockwise.

 

Right image:

This should have a tiny dot in the middle to tell you it is flowing away from you, the magnetic field circulates clockwise.

 

This method helps to remember it (the right hand rule):

 

A Wire carrying a current in a magnetic field will experience a force

If you put a current carrying wire into an external magnetic field (maybe between two magnets) the field around the wire and the field from the magnets interact. The field lines from the magnet contract to form a 'stretched catapult' effect where the flux lines are closer together.

 

It looks like this:

When you put it in the magnetic field, there is a force on the wire. As you can see, there is a dot in the middle so the current is flowing away into the page. There is no force when the current is parallel to the field lines because the fields act in two opposite directions cancelling out.

 

The direction of the force is always perpendicular to both the magnetic field and the current.

 

The resultant force is upwards. If you ever want to know which direction the force is in, use the left hand rule (fleming's left hand rule):

Thumb= direction of force.

First finger (pointy finger)= direction of magnetic field

Second finger= direction of current.

 

Th (fa) = Force

First=field

SeCond=Current.

 

So in the picture above the current is flowing clockwise, to the right. Point your second finger to the right and your thumb points up for the force. The force would be downwards if your second finger was pointing to the left.

 

The size of the force is given by F=BIl

The size of the force, F, on a current carrying wire at right angles to a magnetic field is proportional to the current, I, the length of the wire in a field, l, and the strength of the magnetic field, B.

 

So that makes :

 

F=BIl (effbill)

 

It's defined by:

 

The force on one metre of wire carrying a current of one amp at right angles to the magnetic field.

 

Magnetic field strength is also called flux density and it's measured in teslas, T. Magnetic field strength is a vector quantity since it has direction and magnitude.

 

1 Tesla= Wb/m^2

 

The forces on a loop can be used to make a motor!

Imagine a wire carrying a current is made into a loop. The loop in then placed between two magnets with an attractive force (n/s). The force from the magnets will make the loop rotate.

Use the left hand rule, so for the magnet on the left, your thumb should be pointing up so the force is upwards but as the current goes past the magnet on the right, your hand should be upside down and the force is downwards because the direction of the current changes as it is in a loop. It doesn't mean the current starts flowing around the circuit the other way, it means the direction has changed from your viewpoint. Because the force is opposite for each end of the loop it rotates.

If the loop were to rotate for a half turn then the current would be in the opposite direction to what is was originally and the force would be countered stopping the rotation.

By using a split-ring commutator, the current in the loop can be reversed each time the loop becomes vertical. This makes the loop rotate steadily and it is otherwise known as a motor!