Magnetic Fields Flashcards
What is a magnetic field?
A magnetic field is a region where a force is exerted on magnetic materials
What can magnetic fields be represented by?
Magnetic fields can be represented by field lines (also called flux lines)
In what direction do magnetic field lines go in?
Field lines go from the north to the south pole of a magnet
The closer together the magnetic field lines…
the stronger the field
What is there around a wire carrying electric current?
There is a magnetic field around a wire carrying electric current
What happens when current flows through a wire?
When current flows in a wire or any other long straight conductor, a magnetic field is induced around the wire
Describe the field lines of the magnetic field around a a current carrying wire
The field lines are concentric circles centred on the wire
How can you work out the direction of the magnetic field around a current carrying wire?
You can work out the direction of the magnetic field around a current carrying wire using the right hand rule
Explain how to use the right-hand rule
1- Stick your right thumb up like you’re hitching a lift
2- Your thumb points in the direction of conventional current
3- Your curled fingers point in the direction of the field
What will a wire carrying a current in a magnetic field experience?
A wire carrying a current in a magnetic field will experience a force
Explain what happens if you put a current carrying wire into an external magnetic field
If you put a current-carrying wire into an external magnetic field (eg. between two magnets) the field around the wire and the field from the magnets are added together. This causes a resultant field - lines closer together show where the magnetic field is stronger. These bunched lines cause a ‘pushing’ force on the wire
What is the direction of the force on a current carrying wire in an external magnetic field?
The direction of the force is always perpendicular to both the current direction and the magnetic field, its given by Fleming’s left hand rule
What is the size of the force on a current carrying wire in an external magnetic field if the current is parallel to the field lines?
If the current is is parallel to the field lines the size of the force is 0N - there is no component of the magnetic field perpendicular to the current
Explain how to use Flemings left hand rule
- The first finger points in the direction of the external uniform magnetic field (N to S)
- The second finger points in the direction of the conventional current (+ to -)
- The thumb points in the direction of the force in which motion takes place
What is the force on a wire proportional to?
The force on a current-carrying wire at a right angle to an external magnetic field is proportional to the magnetic flux density (B)
Define magnetic flux density (B)
Magnetic flux density is defined as the force on one metre of wire carrying a current of one amp at right angles to the magnetic field
Where does the equation F=BIl come from?
When current is at 90 degrees to the magnetic field, the size of the force (F) is proportional to the current (I), the length of the wire in the field (l), as well as the flux density (B). This gives the equation F=BIl
Is flux density a scalar or vector quantity?
Flux density is a vector quantity with both a direction and a magnitude. Its measured in teslas (T)
What are each of the variables in the equation F=BIl?
- F is the force
- I is the current
- l is the length of the wire in the field
- B is the flux density
What is 1 tesla equal to in terms of other units?
1 tesla = Wb/m^2
What is Wb (weber) the unit of?
Wb is the unit of the number of flux lines
Explain the method of the practical for investigating flux density (F=BIl)
1- A square hoop of metal wire is positioned so that the top of the hoop, length l, passes through the magnetic field, perpendicular to it. When a current flows, the length of wire in the magnetic field will experience a downwards force (Fleming’s left hand rule)
2- The power supply should be connected to a variable resistor so that you can alter the current. Zero the digital balance when there is no current through the wire so that the mass reading is due to the electromagnetic force only. Turn on the power supply
3- Note the mass and the current. Use the variable resistor to change the current and record the new mass - do this for a large range of currents. Repeat this until you have 3 mass readings for each current. Calculate the mean for each mass reading
4- Convert your mass readings into force using F=mg. Plot the data on a graph of force (F) against current (I). Draw a line of best fit
5- Because F=BIl, the gradient of your graph is equal to B*l. Measure the gradient, then divide by length l to get a value for B
6- Alternatively, you could vary the length of wire perpendicular to the magnetic field by using different sized hoops. You could also keep current and wire length the same and instead vary the magnetic field by changing the strength of the magnets
What acts on charged particle in a magnetic field?
A force acts on a charged particle moving in a magnetic field. This is why a current-carrying wire experiences a force in a magnetic field - electric current in a wire is the flow of negatively charged electrons
What is the formula used to calculate the force on a current-carrying wire in a magnetic field that is perpendicular to the current?
F=BIl
What is electric current?
Electric current (I) is the flow of charge (Q) per unit time (t). So I = Q/t
What velocity does a charged particle which moves a distance l in time t have?
A charged particle which moves a distance l in time t has a velocity, v=l/t so l=vt
State the formula used to calculate the force acting on a single charged particle moving through a magnetic field where its velocity is perpendicular to the magnetic field
F=BQv
- F is the force in N
- B is the magnetic flux density in T
- Q is the charge on the particle in C
- v is the velocity of the particle in ms^-1
Derive the equation F=BQv
F = BIl = BQ/Tvt so F=BQv
In many exam questions what is the value of Q in the formula F=BQv?
Q is the magnitude of the charge on an electron which is 1.6*10^-19C
How are charged particles in a magnetic field deflected?
Charged particles in a magnetic field are deflected in a circular path
What does Fleming’s left hand rule say?
Fleming’s left hand rule says that the force on a moving charge in a magnetic field is always perpendicular to its direction of travel. Mathematically this is the condition for circular motion
What is the difference when using Fleming’s left hand rule for charged particles?
To use Fleming’s left hand rule for charged particles use your second finger (normally current) as the direction of motion for a positive charge. If the particle carries a negative charge point your second finger in the opposite direction to its motion
What is the force due to the magnetic field (F=BQv) experienced by a particle travelling through a magnetic field independent and dependent of?
It is independent of the particle’s mass but the centripetal acceleration it experiences will depend on the mass from Newton’s second law of motion
How can the radius of the circular path followed by a charged particle in a magnetic field be found?
The radius of the circular path followed by a charged particle in a magnetic field can be found by combining the equations for the force on a charged particle in a magnetic field and for the force on a particle in a circular orbit
Derive the equation for calculating the radius of the circular path followed by a charged particle in a magnetic field
F=mv^2/r and F=BQv so mv^2/r=BQv which gives r=mv/BQ
How does the radius of the circular path followed by a charged particle in a magnetic field change as the mass or velocity of the particle increases?
The radius increases (the particle is deflected less) if the mass or velocity of the particle increases
- r=mv/BQ
How does the radius of the circular path followed by a charged particle in a magnetic field change if the strength of the magnetic field?
The radius decreases (the particle is deflected more) if the strength of the magnetic field or the charge on the particle increases
- r=mv/BQ
What is the magnetic flux density also sometimes called?
The magnetic flux density is also sometimes called the strength of the magnetic field
Cyclotrons make use of…
circular deflection
What are cyclotrons used for?
- Circular deflection is used in particle accelerators such as cyclotrons
- Cyclotrons have many uses, for example in medicine. Cyclotrons are used to produce radioactive tracers or high-energy beams of radiation for use in radiotherapy
What is a cyclotron made up of?
A cyclotron is made up of two hollow semi-circular electrodes with a uniform magnetic field applied perpendicular to the plane of the electrodes, and an alternating potential difference applied between the electrodes
Explain how a cyclotron works
- Charged particles are fired into one of the electrodes. The magnetic field makes them follow a semi-circular path and then leave the electrode
- An applied potential difference between the electrodes accelerates the particles across the gap until they enter the next electrode
- Because the particle’s speed is slightly higher, it will follow a circular path with a larger radius before leaving the electrode again
- The potential difference is reversed so the particle is accelerated again before entering the next electrode. This process repeats as the particle spirals outwards, increasing in speed, before eventually exiting the cyclotron
What can the magnetic flux be thought of?
Think of the magnetic flux as the total number of field lines
What is magnetic flux density?
Magnetic flux density (B) is a measure of the strength of a magnetic field. It helps to think of it as the number of field lines per unit area
State the equation used to calculate the total magnetic flux (Φ)
The total magnetic flux (Φ) passing through an area A perpendicular to a magnetic field B is defined as:
Φ = BA
- Φ is magnetic flux (Wb)
- B is the magnetic flux density (T)
- A is the area (m^2)
What is induced in conductors when they cut magnetic flux?
Electromotive forces are induced in conductors when they cut magnetic flux
What occurs if there is relative motion between a conducting rod and a magnetic field?
If there is relative motion between a conducting rod and a magnetic field, the electrons in the rod will experience a force which causes them to accumulate at one end of the rod. This induces an electromotive force (emf) across the ends of the rod, this is called electromagnetic induction
How can you induce an emf in a flat coil or solenoid?
You can induce an emf in a flat coil or solenoid by:
- moving the coil towards or away from the poles of a magnet
- moving a magnet towards or away from the coil
In either case the emf is caused by the magnetic field or magnetic flux that passes through the coil changing. If the coil is part of a complete circuit, an induced current will flow through it
How does the emf induced change as there are more turns in a coil of wire?
More turns in a coil of wire mean a bigger emf will be induced
When you move a coil in a magnetic field what does the size of the emf induced depend on and hence what is flux linkage?
When you move a coil in a magnetic field, the size of the emf induced depends on the magnetic flux passing through the coil (Φ) and the number of turns in the coil that cut the flux (N). The product of these is called the flux linkage
State the equation used to calculate flux linkage
For a coil with N turns, perpendicular to a field with flux density B, the flux linkage is given by:
NΦ=BAN
- N is the number of turns in the coil that cut the flux
- A is the area
- B is the magnetic flux density
- Φ is the magnetic flux passing through the coil
What is the unit of flux linkage and the magnetic flux?
Weber (Wb)
Flux linkage is sometimes given in weber-turns or Wb turns
What does the rate of change in flux linkage tell us?
The rate of change in flux linkage tells you how strong the electromotive force will be in volts
What emf does a change in flux linkage of one weber per second induce?
A change in flux linkage of one weber per second will induce an electromotive force of 1 volt in a loop of wire
When is the equation NΦ=BAN applicable?
This equation can only be used when the magnetic flux is perpendicular to the area you’re interested in
How do we calculate flux linkage when the magnetic flux isn’t perpendicular to the area you’re interested in?
When the magnetic flux isn’t perpendicular to the area you’re interested in, you need to use trig to resolve the magnetic field vector into components that are parallel and perpendicular to the area
State the equation used to calculate the magnetic flux for a single loop of wire when B is not perpendicular to the area
Φ=BAcosθ
- θ is the angle between the field and the normal to the plane of the loop (*See page 144 in the revision guide for a visual representation of where to find θ)
State the formula used to calculate the flux linkage for a coil with N turns when B is not perpendicular to the area
NΦ=BANcosθ
What does the angle of a coil in a magnetic field affect?
The angle of a coil in a magnetic field affects the induced emf
Explain the method of the practical for investigating the effect of angle to the flux lines on effective magnetic flux linkage
1- The stretched metal spring acts as a solenoid and is connected to an alternating power supply (so the flux through the search coil is constantly changing). The search coil should have a known area and a set number of loops of fine wire. It is connected to an oscilloscope to record the induced emf in the coil
2- Set up the oscilloscope so that it only shows the amplitude of the emf as a vertical line (ie. turn off the time base)
3- Position the search coil so that it is about halfway along the solenoid. Orientate the search coil so that it is parallel to the solenoid (and its area is perpendicular to the field), then record the induced emf in the search coil from the amplitude of the oscilloscope trace
4- Rotate the search coil so its angle to the solenoid changes by 10 degrees. Record the induced emf and repeat until you have rotated the search coil by 90 degrees
5- You’ll find that as you turn the search coil, the induced emf decreases. This is because the search coil is cutting fewer flux lines as the component of the magnetic field perpendicular to the area of the coil gets lower, so the total magnetic flux passing through the search coil is lower. This means that the magnetic flux linkage experienced by the coil is lower
6- Plot a graph of induced emf against θ. The induced emf should be maximum at 0 degrees and a zero at 90 degrees
What does Faraday’s law link?
Faraday’s law links the rate of change of flux linkage with emf
State Faraday’s law
Faraday’s law states that the induced emf is directly proportional to the rate of change of flux linkage
Write Faraday’s law as an equation
ε = flux linkage change / time taken = N*ΔΦ/Δt
- ε is the magnitude of induced emf
- N=1 if it’s just a loop, not a coil
Draw a graph of flux linkage (NΦ) against time
See page 146 in the revision guide
What is the gradient of a graph of flux linkage (NΦ) against time (t)?
Gradient = emf
What is the area under a graph of emf against time equal to?
Area = Flux linkage change (NΔΦ)
What can be said if a graph of flux linkage against time is flat?
If the line is flat the gradient is 0 and no emf is induced
State Lenz’s law
Lenz’s law states that the induced emf is always in such a direction as to oppose the change that caused it
State the formula that works for both Faraday’s and Lenz’s law that comes from combining both laws
ε = - flux linkage change / time taken = -N*ΔΦ/Δt
- The minus sign shows the direction of the induced emf
How does the idea that an induced emf will oppose the change that caused it agree with the principle of the conservation of energy?
The idea that an induced emf will oppose the change that caused it agrees with the principle of the conservation of energy - the energy used to pull a conductor through a magnetic field against the resistance caused by magnetic attraction, is what produces the induced current
How can we find the direction of an induced emf and current in a conductor travelling at right angles to a magnetic field?
Lenz’s law can be used to find the direction of an induced emf and current in a conductor travelling at right angles to a magnetic field
Explain how to use Lenz’s law to find the direction of an induced emf and current in a conductor travelling at right angles to a magnetic field
- Lenz’s law says that the induced emf will produce a force that opposes the motion of the conductor - in other words a 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
- Point your first finger in the direction of the field. 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
What is an alternator?
An alternator is a generator of alternating current
What is a generator?
Generators or dynamos convert kinetic energy into electrical energy, they induce an electric current by rotating a coil in a magnetic field
What are slip rings and brushes used for in a generator?
Slip rings and brushes are used to connect the coil to an external circuit
How does the output voltage and current change in a generator?
The output voltage and current change direction with every half rotation of the coil, producing alternating current (ac)
What is the phase difference of flux linkage and induced voltage?
Flux linkage and induced voltage are 90 degrees out of phase
What is the flux linkage?
Flux linkage is the amount of flux cut by the coil
State the formula used to calculate flux linkage
NΦ=BANcosθ
- θ is the angle between the normal to the coil and the flux lines
How does the flux linkage vary as the coil rotates in an alternator?
As the coil rotates θ changes so the flux linkage varies sinusoidally between +BAN and -BAN
What does how fast θ changes depend on in an alternator?
How fast θ changes depends on the angular speed (ω) of the coil so the flux linkage equation can be rewritten as:
- flux linkage = NΦ = BANcosωt where θ=ωt
What does the induced emf depend on in an alternator?
The induced emf (ε) depends on the rate of change of flux linkage (Faraday’s law) so it also varies sinusoidally
State the equation for the emf at time t in an alternator
ε = BANωsin(ωt)
Alternating current is….
constantly changing
What is an alternating current?
- An alternating current or voltage is one that changes direction with time
- This means the voltage across a resistance goes up and down in a regular pattern - some of the time its positive and some of the time its negative
How can you display the voltage of both an alternating and direct current?
You can use an oscilloscope to display the voltage of an alternating current and direct current too. Oscilloscopes are just like really fancy voltmeters, the vertical height of the trace at any point shows the input voltage at that point
How can you use the grid on an oscilloscope screen?
The oscilloscope screen has a grid on it which allows you to select to how many volts per division you want the y-axis scale to represent using the Y-gain control dial, e.g. 5V per division
What are the two different types of waveforms given by alternating and direct currents?
- An alternating current (ac) source gives a regularly repeating sinusoidal waveform
- A direct current (dc) source is always at the same voltage so you get a horizontal line
If you turn off the time base, how can an oscilloscope display ac voltage and dc voltage?
Oscilloscopes can display ac voltage as a vertical line and dc voltage as a dot if you turn off the time base
Which 3 main measures can be found using an oscilloscope trace?
Using an oscilloscope trace you can find:
- Time period (T)
- The peak voltage (V0)
- The peak to peak voltage
Draw a general oscilloscope trace and label the time period, the peak voltage and the peak to peak voltage
See page 148 in the revision guide
Explain the general difference in power output for for an ac supply and a dc supply of 2V
An ac supply with a peak voltage of 2V will be below 2V most of the time. This means that it won’t have as high a power output as a 2V dc supply.
To compare an ac and a dc power supply properly, what do we need to calculate?
To compare them properly we need to calculate the root mean square (rms) voltage
State the formula used to calculate the rms voltage (Vrms) for a sine wave
Vrms = V0/√2
- V0 is the peak voltage in volts
State the formula used to calculate the rms current (Irms) for a sine wave
Irms = I0/√2
- Io is the peak current in amps
How do we calculate the average power of an ac supply?
Average power = Irms*Vrms
How do we find the time period from an oscilloscope trace and hence the frequency?
- The period is found by measuring the distance between successive peaks along the time axis
- To find the frequency use f = 1/T
What type of supply is the UK’s mains electricity supply?
The UK’s mains electricity supply is an alternating current supply around 230V. 230V is the rms value
What do transformers work by?
Transformers work by electromagnetic induction
What are transformers?
Transformers are devices that make use of electromagnetic induction to change the size of the voltage for an alternating current
Explain how transformers work
- An alternating current flowing in the primary/input coil produces magnetic flux
- The changing magnetic field is passed through the iron core to the secondary/output coil where it induces an alternating voltage of the same frequency as the input voltage
- From Faraday’s law the induced emfs in both the primary and the secondary coils can be calculated
State the formulas used to calculate the emf induced in both the primary and secondary coils of a transformer
Primary coil: Vp = NpΔΦ/Δt
Secondary coil: Vs = NsΔΦ/Δt
N is the number of turns in a coil
State the transformer equation for an ideal transformer
Ns/Np=Vs/Vp
N is the number of turns in a coil
State the difference between Step-up and Step-down transformers
- Step-up transformers increase the voltage by having more turns on the secondary coil than the primary
- Step-down transformers reduce the voltage by having fewer turns on the secondary coil than the primary
State the relationship between transformers and efficiency
Transformers are not 100% efficient. If a transformer was 100% efficient the power in would equal the power out
State the equation linking current and voltage for an ideal transformer
IpVp = IsVs or Is/Ip = Vp/Vs
In practice why will there be small losses of power from a transformer?
In practice there will be small losses of power from a transformer mostly due to eddy currents in the transformers iron core
What are eddy currents?
Eddy currents are looping currents induced by the changing magnetic flux in the core. They create a magnetic field that acts against the field that induced them reducing the field strength. They also dissipate energy by generating heat
How can the effect of eddy currents be reduced?
The effect of eddy currents can be reduced by laminating the core with layers of insulation
How can we minimise the heat generated by resistance in the coils of a transformer?
Heat is also generated by resistance in the coils of a transformer and this can be minimised by using thick copper wire which has a low resistance
What is the efficiency of a transformer?
The efficiency of a transformer is simply the ratio of power out to power in
State the formula used to calculate the efficiency of a transformer
Efficiency = IsVs/IpVp
This gives the efficiency as a decimal so multiply it by 100 to get it as a percentage
State the formula which can be used for transformers by combining both of the ideal transformer equations together
Vp/Vs = Np/Ns = Is/Ip
State the relationship between transformers and the national grid
Transformers are an important part of the national grid
Explain how the national grid works
Electricity from power stations is sent around the country in the national grid at the lowest possible current because the power losses due to the resistance of the cables is equal to P=I^2R so if you double the current transmitted you quadruple the power lost. Since power = current*voltage a low current means a high voltage
How are transformers used as part of the national grid?
Transformers allow us to step up the voltage to around 400000V for transmission through the national grid and then reduce it again to 230V for domestic use
