Fields (5): Electromagnetic Induction Flashcards
What is the phenomenon called where an electric current is generated in a wire by moving it through a magnetic field?
Electromagnetic induction
Describe how electromagnetic induction works
- A wire is moved across a magnetic field between two magnets
- This induces an electromotive force, emf, into the wire
- If this wire is part of a complete circuit then th induced emf forces electrons round the circuit -> a current is read
How can the induced emf in electromagnetic induction be increased?
- Moving the wire faster
- Using a stronger magnet
- Making the wire into a coil and pushing the magnet in or out
In what scenario will an emf not be induced into a wire that moves through a magnetic field?
If the wire is parallel to the field lines as it moves through the field
Will a current always be induced when a magnet is moved relative to a conductor?
No, the conductor has to be part of a complete circuit in order for a current to be induced
Does the emf induced in a wire act in the same way as the emf of a battery?
No - the emf of a battery is constant whereas the emf induced in a wire becomes zero when the relative motion between the magnet and the wire ceases
What does an electric current do when it is induced in a wire?
The electric current transfers energy from the source of the emf to the other components in the circuit
Why will a spinning/moving magnet stop, even in the absence of other resistive forces, when it is in a magnet-coil system?
- The spinning magnet is doing work on the electrons in the wire/coil
- As an emf is induced, current flows in the coil
- The current transfers energy from the source of emf to the other components
- Therefore, work must be done to keep the magnet spinning
Energy transferred from the coil/wire to the components in its circuit is equal to…?
The work done on the magnet (inducing the emf) to keep it spinning
What does a wire contain?
Electrons
When electrons move through a magnetic field what do they experience?
A force
What rule do you need to use for generators?
Flemings right hand rule
Thumb - motion of conductor
First finger - field
Second finger - Current
What rule to you need to use for the motor effect?
Flemings left hand rule
What is the name of a wire that has been strung into loops?
A solenoid
What rule can be used to determine the direction of a magnetic field/direction of current in a solenoid?
Right hand grip rule
State Lenz’s Law
The direction of the induced current is always such as to oppose the change that causes the current
What is the conservation law that explains Lenz’s law?
Conservation of energy
What happens when the north pole of a magnet is push into a solenoid?
- A current is induced into the coils of the solenoid
- As you have a current flowing through a wire a magnetic field is produced
- The magnetic field produced is one that opposes the motion of the magnet
- Therefore the end of the solenoid closest to the north pole of the magnet becomes a north pole itself
NB - if this wasn’t the case then the coil would pull the north pole in even faster which would generate a stronger magnetic field in the wire, pulling the north pole in even faster and etc.
What happens when the north pole of a bar magnet is brought out of a solenoid?
- A current is induced into the coils of the solenoid in the opposite direction to when the north pole entered the solenoid
- A magnetic field is produced in the opposite direction and is one that opposes the motion of the magnet
- Therefore the end of the solenoid closest to the north pole of the magnet becomes a south pole
State Faradays Law of electromagnetic induction
The induced emf in a circuit is equal to the rate of change of flux linkage through the circuit
Describe what happens when a conducting poll vertical across metal rails is forced right, in a magnetic field going into the page?
Electromagnetic induction
- Relative movement of a conductor in a magnetic field
- Induces a current upwards
Lenzs Law - the direction of the induced current is always such that it opposes that change that caused the current
Motor effect
- Current flowing through the wire in a magnetic field causes a force on the wire to the left, F = BIl
Due to this opposing force being produced, an equal but opposite force must be applied to the conducting poll to keep it moving in the field
What is the equation for the work done by the applied force to move a conducting rod across a magnetic field?
W = Fd
= BIl(delta)s
What is the equation for the charge transfer across a conducting rod being moved across a magnetic field in time, t?
Q = I(delta)t
What is the equation for the induced emf in a conductor be forced across a magnetic field, with work done, W, and charge transfer across, Q? How do you derive it?
induced emf = W/Q
= BIl(delta)s / I(delta)t
= Bl(delta)s / (delta)t
l(delta)s = A, the area swept out by the conductor in time (delta)t
induced emf = BA/(delta)t
How would you describe magnetic flux?
The area swept out by a conductor in a magnetic field with flux density B
What is the equation for magnetic flux?
magnetic flux, theta = BA
It what scenario only is the equation for magnetic flux true?
When the magnetic field is normal/perpendicular to A
When is magnetic flux linkage used?
When a coil is sweeping across a magnetic field
What is the equation for magnetic flux linkage?
N(theta) = NBA
where:
- N is the number of turns of the coil
- B is the magnetic field perpendicular to area A
State the unit of magnetic flux
Weber, Wb
= Tm^2
Describe flux density using theta = BA?
Flux density is the flux per unit area, passing at right angles through the area
If a field is not at right angles to the direction of motion of the conductor, what do you have to do
- The normal is drawn -> the direction of motion of the conductor
- Need to resolve the magnetic field to find the perpendicular component of the magnetic field
- The hypotenuse is = B
- Need to think about resolving all the field lines
- Resolve in the direction of motion of the conductor
If the magnetic field is not perpendicular to the line of motion of the conductor/coil, what is the equation used for magnetic flux?
theta = BAcos(theta)
NB - thetas are not the same
If the magnetic field is not perpendicular to the line of motion of the conductor/coil, what is the equation used for magnetic flux linkage?
N(theta) = BANcos(theta)
When a coil is perpendicular to the magnetic field, the flux linkage = …?
N(theta) = BAN
When a coil is turned through 180 degrees to the magnetic field, the flux linkage = …?
- BAN
When a coil is parallel to the magnetic field, the flux linkage = …?
= 0
What is the equation that states Faradays Law?
Induced emf, E = -N(d(theta)/dt)
where
N(d(theta)/dt) = is the change of flux per second
Why is there a negative sign in front of N(d(theta)/dt) for the value of the induced emf?
To represent that the induced emf acts in such a direction as to oppose the change that causes it -> Lenz’s Law
What is the equation for the induced emf in a conductor moving at right angles to the magnetic field involving the speed of the conductor?
induced emf, E = Bl(delta)s/(delta)t
as delta s/ delta t = v
induced emf, E = BIv
Describe the changes that occur when a rectangular coil, N turns, width w and length l, is moved through a uniform magnetic field B at a constant speed, v
The time taken for the coil to enter the field completely:
= coil width/speed = w/v
During this time the flux linkage increases steadily from 0 to BNlw. Therefore, change in flux linkage per second is:
N(delta)theta/ (delta)t = BNlw/ w/v = BNlv
An emf is induced in the coil -> current
When the coil is completely in the field the flux linkage throughout it does not change so the emf induced = 0. This because the emf induced in the leading side is cancelled out by the emf induced in the trailing side.
Describe the graph of induced emf against time for a rectangular coil of wire entering a magnetic field up to the time when it is fully in the field
Straight line across from the value of induced emf
Describe the graph of flux linkage against time for a rectangular coil of wire entering a magnetic field up to the time when it is fully in the field
Straight line increasing from 0 to value of flux linkage
Describe the basic set up of a simple ac generator
A rectangular coil that spins in a uniform magnetic field
Does the flux linkage change continuously in an ac generator? Why?
Yes. This is because the angle between the normal of the rectangular coil and the field lines is constantly changing
What is the equation for the angle, theta, at any time in a simple ac generator?
theta = 2(pi)ft
What is the equation for the emf in a rectangular rotating coil in a generator at time, t?
E = E0sin2(pi)ft
OR
E = E0sin(omega)
where omega = 2(pi)f
What does E0 stand for?
Peak emf - this is the emf from the equilibrium to a peak or trough
How would you increase peak emf in an ac generator?
- Increasing the frequency of rotation of the coil (its speed)
- Using a stronger magnet
- Using a bigger coil
- Using a coil with more turns
Describe the graph of emf against time for an ac generator
Follows the shape of a sine graph:
If at t = 0 the coil is parallel to the field:
- Emf is a maximum when the coils motion is perpendicular to the field, at 1/4f and 3/4f
- Emf is a minimum when the coils motion is parallel to the field, at 0, 1/2f, 1/f
Describe the graph of flux linkage against time for an ac generator
Follows the shape of a cos graph:
NOT THE SAME AS THE RATE OF CHANGE OF FLUX LINKAGE = EMF
If at = 0 the coil is parallel to the field:
- Flux linkage is a maximum at t = 0, 1/2f and 1/f, when the coil is parallel to the field
- Flux linkage is a minimum at t = 1/4f and 3/4f, when the coil is perpendicular to the field
What is the equation for th eemf induced in a rotating coil?
E = BAN(omega)sin(omega)t
When flux linkage = 0, the rate of change of flux (emf) is…?
A maximum
When flux linkage is a maximum, the rate of change of flux (emf) i…?
0
In what apparatus is a back emf produced?
electric motor
What is the back emf equal to?
The emf induced in the spinning coil of the electric motor
Why is the induced emf called the back emf?
As it acts against the applied pd to the motor in accordance with Lenz’s Law
What is the equation for the voltage around the motor coil at any point?
V - emf = IR
V - pd voltage supplied to the motor
Emf - induced emf in the coil that opposes the applied pd across the motor
I - current through the motor coil
R - The circuit resistance
How does the the current of a motor coil change with speed if the coil?
Speed increases -> current decreases as emf increases
Speed decreases -> current increases as emf decreases
What is the relationship between speed of a coil in an electric motor and the induced emf?
Proportional
What is the equation for the electrical power supplied by your electric motor?
IV = IE (electrical power transferred to mechanical power) + I^2R (electrical power wasted due to circuit resistance)
What is the definition of an alternating current?
One that repeatedly reverses its direction
When a coil rotates in a magnetic field what type of current is produced?
Alternating current
What apparatus do we use to observe the variations in voltage/current in a circuit?
An oscilloscope
What is the x-axis called on an oscilloscope?
The time-base
What is the y-axis called on an oscilloscope?
Y - sensitivity
What will alternating current look like on an oscilloscope when the time base is turned off?
A straight line from +E0 to -E0
Why would we turn off the time base of an oscilloscope?
As it makes it easier to take measurements
What is the definition of the peak voltage, V0/I0?
On an oscilloscope: Distance from equilibrium to the peak or trough of the wave
What is the definition of peak to peak voltage/current?
On an oscilloscope: Maximum distance from the peak to the trough of the wave
What is the shape of how the mains pd varies with time?
Sinusoidal
What is the frequency of mains electricity in the UK?
50Hz
What is the peak voltage of mains electricity in the UK?
325V
What is the equation showing the heating effect of current/electrical power supplied to a component?
P = I^2R
What is the shape of how the current supplied by an alternating source changes with time?
sinusoidal
For a sinusoidal current, how t power supplied by the source change?
P = I^2R
Power varies with a shape the same as current but does not go negative (as any -ve current squared is positive) and reaches a much higher peak compared to current (slightly more than double)
What is the mean power supplied by a source equal when the source supplies alternating current?
Half the peak power = 1/2 I0^2R
What is the value of direct current/voltage that would give the same power as the mean power in alternating current/voltage?
root mean square value, Irms
What is the root mean square value of an alternating current?
The value that is equivalent to the value of direct current that would give the same heating effect as the alternating current in the same resistor
What are the equations for Vrms and Irms?
Vrms/Irms = 1/root(2)V0/I0
How would you calculate your peak power supplied to a resistor of known resistance?
P = I0^2R = V0^2/R = I0V0
How would you calculate your mean power supplied to a resistor of known resistance?
P = Irms^2R = Vrms^2/R = Irms x Vrms
Describe the set up of a transformer
- A primary coil is attached to an input voltage (produces an alternating current)
- A secondary coil is attached to an output voltage
- An iron core links them
Describe briefly how a transformer works
Transformers are used to change an alternating pd to a different peak value
- When the primary coil is connected to an alternating pd, an alternating magnetic field is produced in the core
- The field passes through the secondary coil causing an alternating flux linkage (different to flux linkage across the primary coil)
- An alternating emf is produced in the secondary coil
State the transformer rule
The ratio of the voltage in the primary coil to the secondary coil is the same as the ratio of the number of coils in the primary coil to the secondary coil
What is a step-up transformer?
Has more turns on the secondary coil, thereby a greater output voltage than input voltage (but smaller current)
What is a step-down transformer?
Has more turns on the primary coil, therefore a smaller output voltage comparative to the input voltage (but greater current)
Are transformers generally efficient?
Yes, they are extremely efficient (almost 100% efficiency)
What are the 3 factors that affect the efficiency of a transformer?
- Resistance of the windings
- Lamination of the core
- Nature of the core
How does the resistance of the windings affect the efficiency of a transformer?
Low resistance windings (material used for coils) mean that the power wasted due to the heating effect of the current is reduced
How does the lamination of the core affect the efficiency of a transformer?
A laminated core consists of layers of iron separated by layers of insulating material. This reduces the size of the induced currents, eddy currents, in the core so magnetic flux is as high as possible. Also the heating effect of the induced currents in the core is reduced.
How does the nature of the core affect the efficiency of a transformer?
A soft iron core is much more efficient that a hard metal core. This is because it is able to be easily magnetised and demagnetised which reduces the power lost due to repeated magnetisation and demagnetisation.
Do we transmit electricity at high or low voltage? Why?
High voltages - As transmission of electrical power over long distances is much more efficient at a high voltage
Why, using equations, is it more efficient to transmit electricity using high voltages?
For transmission of the same power through cables of a constant resistance:
Using low voltages
P = IV
Your current would be high
P = I^2R
Your power dissipated would be high
Using high voltages
P = IV
Your current would be low
P = I^2R
Your power dissipated would be low
NB - As P = V^2/R the power dissipated is much smaller for higher voltages
