Magnetic Fields Flashcards
How is a magnetic field similar to electric and gravitational fields?
It’s a region in which a force acts
What is a magnetic field?
A region in which a force acts on magnetic materials or magnetically susceptible materials
How do you represent magnetic fields?
Field lines (also called flux lines)
What is the direction of field lines for a magnetic field?
From the north to the south pole of a magnetic
The closer field lines are together, the…?
Stronger the field is
How is a magnetic field induced around a wire?
When current flows in a wire, it induces a magnetic field
Describe the field lines for a magnetic field induced around a wire?
They are concentric circles centred around the wire
What rule do you use to work out direction of magnetic field in a current-carrying wire?
Right-hand rule (by wrapping hand around with thumb pointing in direction of current, direction of curled fingers shows direction of magnetic field?)
What is the magnetic field of a solenoid similar to?
Magnetic field of a bar magnet
Describe the magnetic field formed when you place a wire between 2 external magnetic fields (e.g. 2 magnets)?
The field around the wire and the fields from the magnets are added together, resulting in a resultant field
For the magnetic field around a current-carrying wire, what does a solid dot show?
• = current flowing out of the page, towards the reader
For the magnetic field around a current-carrying wire, what does a solid dot show?
⊗ = current going into the page, away from the reader
For the magnetic field of a current-carrying wire between 2 magnets, which direction is the resultant force of the field?
Perpendicular to both current direction and magnetic field
What is the resultant force of magnetic field of a current-carrying wire between 2 magnets equal to if the current is parallel to the field lines?
Resultant force = 0N
For Fleming’s left-hand rule, what does the first finger denote?
First finger = direction of uniform magnetic Field
For Fleming’s left-hand rule, what does the second finger denote?
SeCond finger = direction of conventional Current
For Fleming’s left-hand rule, what does the thumb denote?
ThuMb = direction of force (so direction of Motion)
What happens to a wire when you pass an alternating current through a wire in a magnetic field?
The wire vibrates
Why does a wire vibrate if you pass an alternating current through it in a magnetic field?
Because force is perpendicular to direction of current, so if current is reversed, direction of force is also reversed. Constant reversal of force means that the force is constantly alternating too, so up and down motion of wire
What is the magnetic flux density defined as?
The force on 1 metre of wire carrying a current of 1A at right angles to the magnetic field
What is magnetic flux density proportional to?
The force on a current-carrying wire at right angle to a magnetic field
What are the units of magnetic flux density?
Tesla (T)
Is magnetic flux density a scalar or vector quantity?
Vector, because it has both direction and magnitude
What is 1 tesla equal to?
1 tesla = 1 newton per amp per metre
What is the equation for the force on a current-carrying wire in a field?
F = BIL
F: Force on current-carrying wire
B: Magnetic flux density
I: Current through wire
L: Length of wire
For the equation F = BIL, what is the force?
The maximum force possible (when the wire is at 90° to the magnetic field)
When a current-carrying wire is at 90° to a magnetic field, what is the size of the force on the wire proportional to?
Size of the force on the wire proportional to length of wire and also magnetic flux density
What is the equation for the force acting on a single particle in a magnetic field?
F = BQv
F: Force
B: Magnetic flux density
Q: Charge on particle
v: Velocity of particle
How do you derive the equation for the force acting on a single particle in a magnetic field?
Use the equation the force on a current-carrying wire in a field, F=BIL. Substitute I = Q/t to get F=B(Q/t)vt then cancel the t to get F = BQv
To use Fleming’s left-hand rule for the a charged particle, what do you use the second finger to show?
Second finger = direction of motion for a positive charge
If the particle is negative, point your second finger in the opposite direction to its motion
What is the equation for the acceleration of a particle travelling through a magnetic field?
A = v^2/r
What is the equation for the force on a particle in a circular path in a magnetic field?
F = mv^2 / r
What is the equation to find the radius of the circular path of a charged particle in a magnetic field?
r = mv / BQ
If the mass or velocity of a particle in a field increases, what affect does this have on the radius of curvature of the particle?
The radius of curvature increases
If the magnetic field strength or charge on a particle in a field increases, what affect does this have on the radius of curvature of the particle?
The radius of curvature decreases
What is the relationship between the radius of curvature of a charged particle in a magnetic field and its mass?
Directly proportional
What is the equation for the frequency of rotation for an object in circular motion?
f = v / 2πr
f: frequency of rotation
v: velocity
2π: distance travelled in each rotation
What does the time it takes for a particle to complete a full circle depend on?
Magnetic flux density
Mass
Charge
What will increasing a particles velocity have an affect on?
Will make it follow a circular path with larger radius, but will take the same amount of time to complete it
What are cyclotrons?
A type of particle accelerator
Give an example of one of the uses of a cyclotron
Medicines (more specifically diagnosis and therapy)
How is a cyclotron used in radiotherapy?
Used to produce radioactive tracers or high-energy beams of radiations for use in radiotherapy
What is radiotherapy?
A cancer treatment that uses high doses of radiation to kill cancer cells and shrink tumors
What is a cyclotron made up of?
2 hollow semicircular electrodes with a uniform magnetic field applied perpendicular to the plane of the electrodes, and an alternating potential difference applied between the electrodes
How does a cyclotron work?
Charged particles are produced and fired into one of the electrodes, where the magnetic field makes them follow a circular path and then leave the electrode (at a faster speed)
What does the applied potential difference between the electrodes in a cyclotron cause?
It accelerates the particle across the gap between the electrodes
What causes the particle in a cyclotron to reach the exit of the cyclotron?
Each time the P.D. accelerates the particle across the gap between the electrodes, the particles speed gets slightly bigger. This causes the radius of the circular path to get bigger until it reaches the exit point
Why is an alternating potential difference used in a cyclotron?
Because if it had a direct potential difference, the particle would only accelerate in one direction across the gap between the electrodes
Why will the particle always spend the same amount of time in each electrode of a cyclotron?
Because the frequency of the circular motion is independent of the radius (meaning the alternate potential difference has the same frequency)
What is magnetic flux density, B?
A measure of the strength of a magnetic field (think of as number of field lines per unit area)
What is the equation for the total amount of magnetic flux passing through an area perpendicular to a magnetic field?
Φ = BA
Φ: Magnetic flux
B: Magnetic flux density
A: Area
What is magnetic flux measured in?
Wb (Webers)
What can magnetic flux be defined as in terms of field lines?
The total number of field lines
What is the difference between magnetic flux density and magnetic flux?
Magnetic flux density is the number of field lines per unit area whereas magnetic flux is the total number of field lines
What is electromagnetic induction?
The process of inducing an e.m.f. in a conductor with relative motion to a magnetic field
When is an e.m.f. induced by a conductor and a magnet?
When the conductor cuts the magnetic flux (perpendicular to magnetic field lines)
What happens to the electrons in a rod if there is relative motion between a conducting rod and a magnetic field?
The electrons will feel a force, which causes them to accumulate at one end of the rod
How can you induce an e.m.f. with a conductor and a magnet, solenoid or flat coil?
Move the conductor inside a stationary magnetic field or vice versa
What causes the e.m.f. to be positive or negative in electromagnetic induction?
It depends on the direction of movement and the way you connect the wires
When a wire coil is moved in a magnetic field, what does the size of the e.m.f. depend on?
The magnetic flux passing through the coil and the number of turns on the coil cutting the flux
What is flux in physics?
The presence of a force field in a specified physical medium
What is flux linkage, NΦ?
The magnetic flux in a coil multiplied by the number of turns on the coil
For a coil of N turns normal (perpendicular) to B, what is the equation for the flux linkage?
Flux linkage = [NΦ] = BAN
Φ: Magnetic flux
B: Magnetic flux density
A: Area of the coil
N: Number of turns on the coil cutting the flux
What is the SI unit of flux linkage?
Wb (Webers)
What does the rate of change of flux linkage tell you?
How strong the e.m.f. will be
What is a change of flux linkage of 1Wb per second equal to?
An e.m.f. of 1 volt in a loop of wire
How do you find the flux linkage at an angle?
You need to resolve the magnetic field vector into components that are parallel and perpendicular to the area using trig
For a single loop of wire when B is not perpendicular to the area, what is the equation for the magnetic flux?
Φ = BA cosθ
Φ: Magnetic flux
B: Magnetic flux density
A: Area of the coil
θ: Angle between the normal to the plane of the coil and the magnetic field
For a coil with multiple turns, what is the equation for flux linkage if B is not perpendicular to the area?
NΦ = BAN cosθ
Φ: Magnetic flux B: Magnetic flux density A: Area of the coil N: Number of turns θ: Angle between the normal to the plane of the coil and the magnetic field
How do you set up the experiment to investigate the flux linkage with a search coil?
Set up a stretched metal spring (as the solenoid) and have a search coil inside it. Below the search coil put a protractor, then attach the search coil to an oscilloscope. Complete the circuit for the stretched metal spring by connecting an alternating current power supply
For the experiment to investigate the flux linkage with a search coil, why do you use an alternating current?
So that the magnitude of the solenoid is constantly changing, meaning the flux through the search coil is changing which can induce an e.m.f.
For the experiment to investigate the flux linkage with a search coil, what 2 things should you know for the search coil?
A known area and a known number of loops of fine wire
Why is the search coil connected to an oscilloscope?
To measure the induced e.m.f. in the coil
For the experiment to investigate the flux linkage with a search coil, how do you set up the oscilloscope?
Set it to only show the e.m.f. as a vertical line (so it ignores the time base)
For the experiment to investigate the flux linkage with a search coil, what is the protractor used for?
To measure the orientation of the normal to the area of the search coil as an angle from the line of the magnetic field
For the experiment to investigate the flux linkage with a search coil, how do you position the search coil?
Halfway along solenoid, but making sure it doesn’t touch. Orientate it so that it is parallel to the solenoid (θ= 0°) and its area is perpendicular to the field
Where is the magnetic field of a solenoid strongest?
In the solenoid
What can be assumed for the magnetic field in a solenoid?
It’s uniform and parallel to the side of the solenoid
What measurement do you take in the experiment to investigate the flux linkage with a search coil?
Record the induced e.m.f. in the search coil from the amplitude of the oscilloscope trace
For the experiment to investigate the flux linkage with a search coil, after you’ve recorded the induced e.m.f at θ= 0°, what do you change?
Rotate the search coil so that its angle to the solenoid and flux lines change by 10°, then record the induced e.m.f. Repeat until θ= 90°
For the experiment to investigate the flux linkage with a search coil, what would you expect to find as you turn the search coil?
You’d expect to see the induced e.m.f decrease
Why does the induced e.m.f. decrease when you rotate the search coil in a solenoid?
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 total magnetic flux passing through the search coil decreases
What is Faraday’s Law?
The induced e.m.f. is directly proportional to the rate of change of flux linkage
What is the equation for Faraday’s Law?
Ɛ = N (ΔΦ / Δt)
Ɛ: Magnitude of induced e.m.f
N: Number of turns on coil
t: Time taken for flux to change
Φ: Change in magnetic flux
For Faraday’s Law, what does the equation Ɛ = N (ΔΦ / Δt) mean in words?
Magnitude of induced e.m.f. = Rate of change of flux linkage
What is the gradient of a flux linkage-time graph equal to?
Magnitude of e.m.f.
What is the area under a magnitude of e.m.f.-time graph equal to?
Flux linkage change
What is the equation for the area of flux a conductor cuts?
A = lvΔt
A: Area of flux object cuts through
l: Length of object
v: Velocity
t: Time taken
What is Lenz’s Law?
The induced e.m.f. is always in such a direction as to oppose the change that caused it (the induced e.m.f. will produce a force that opposes the motion of the conductor)
What principle can be used as proof for Lenz’s Law?
Conservation of energy principle
How does the principle of conservation of energy prove Lenz’s Law?
The energy used to pull a conductor through a magnetic field, against the resistance caused by magnetic attraction, is what produces the induced current
What can Lenz’s Law be used for?
To find the direction of an induced e.m.f. and current in a conductor travelling at right angles to a magnetic field
How do you work out the direction of the induced e.m.f. and the current for a conductor moved down through a perpendicular magnetic field?
Using Fleming’s left-hand rule – Point thumb in direction of force (the resistance so point opposite direction to motion of conductor) and then point first finger in direction of field. The direction your second finger is pointing is direction of induced e.m.f.
When a coil rotates uniformly (where the axis of rotation is perpendicular to direction of field) in a magnetic field, what happens?
The coil cuts the flux and an alternating e.m.f. is induced
What is the equation for flux linkage for a rotating coil?
NΦ = BAN cos ωt
NΦ: Magnetic flux B: Magnetic flux density A: Area of the coil N: Number of turns on coil t: Time ω: Angular speed
As the coil rotates in a magnetic field, what can be said about the flux linkage as θ changes?
The flux linkage varies sinusoidally between +BAN and -BAN
B: Magnetic flux density
A: Area of the coil
N: Number of turns on coil
What does sinusoidally mean?
It follows the same pattern as a sin (or cos) curve
What can be said about how the induced e.m.f. varies when a coil is rotated in a magnetic field?
It varies sinusoidally
What is the equation for the induced e.m.f. of a coil rotated in a magnetic field?
ε = BANωsinωt
ε: Induced e.m.f. B: Magnetic flux density A: Area of the coil N: Number of turns on coil ω: Angular speed t: Time
When a coil is rotated in a magnetic field, what is the phase difference for the graphs of flux linkage/time and induced e.m.f./time?
Flux linkage and induced e.m.f. are 90° out of phase
When a coil is rotated in a magnetic field, at what values of θ is the flux linkage at maximum?
At 0° and 180° (because this means that the coil is cutting the most amount of flux)
When a coil is rotated in a magnetic field, at what values of θ is the flux linkage 0?
90° and 270° (because this means the coil is parallel to the flux, so is not cutting any of the flux)
When a coil is rotated in a magnetic field, at what values of θ is the induced e.m.f. 0?
0° and 180°
When a coil is rotated in a magnetic field, at what values of θ is the induced e.m.f. at maximum?
90° and 270°
When a coil is rotated in a magnetic field, what effect does increasing the speed of rotation have?
It will increase the frequency and increase the maximum induced e.m.f.
(changes are directly proportional)
When a coil is rotated in a magnetic field, what effect does increasing the magnetic flux density (B) have?
It will increase the maximum e.m.f., but has no effect on the frequency
(changes are directly proportional)
How do generators, or dynamos, work?
They convert kinetic energy into electrical energy by inducing an electric current by rotating a coil in a magnetic field
In a generator, what is the purpose of slip rings and brushes?
To connect the coil to an external circuit
Why do generators produce an alternating current?
The output voltage and current change direction from every half rotation of the coil, producing an alternating current
What is an alternating current?
A current that changes direction with time
What does an alternating current mean for the voltage?
The voltage across a resistance goes up and down - normally from positive to negative
For oscilloscope traces, what does the vertical height mean?
The input voltage at that point in time
What is the trace on an oscilloscope made from?
By an electron beam moving across the screen
Why is the time base on an oscilloscope important?
It controls how fast the beam is moved across the screen
What shape of graph would you see on a oscilloscope when measuring the voltage of an alternating current?
The graph would have a regular, repeating sinusoidal shape
What shape of graph would you see on a oscilloscope when measuring the voltage of a direct current?
A straight, horizontal line
How would an oscilloscope display an alternating current voltage with the time base turned off?
As a vertical line
How would an oscilloscope display a direct current voltage with the time base turned off?
As a dot
What are the 3 pieces of information you need to find when analysing an oscilloscope trace?
Time period
Peak voltage
Peak-to-peak voltage
On an oscilloscope trace, how do you find the time period?
You measure the distance between the successive peaks along the time axis gives you the time period (as long as you know the time base)
What equation links frequency and time period?
Frequency = 1 / Time period
How do you find the peak voltage on an oscilloscope trace?
Measure the distance between the horizontal axis and the top of a peak
How do you find the peak-to-peak voltage on an oscilloscope trace?
Measure the distance between the top of a peak above the horizontal axis and the bottom of a peak below the horizontal axis
Why can’t you compare an ac supply with a peak voltage of 2V and a dc supply with a peak voltage of 2V?
Because most of the time, the ac supply voltage will be below 2V
How do you compare an ac supply voltage and a dc supply voltage?
You need to average the ac voltage (by working out the root mean square voltage)
For a sine wave, what is the equation to work out the root mean square voltage of an ac supply?
Vrms = V0 / √(2)
Vrms: Root mean square voltage
V0: Peak voltage
For a sine wave, what is the equation to work out the root mean square current of an ac supply?
Irms = I0 / √(2)
Irms: Root mean square current
I0: Peak current
What is the equation for average power for an ac supply?
average power = Irms x Vrms
Irms: Root mean square current
Vrms: Root mean square voltage
How do you derive the equation for the average power of an ac supply?
It’s the same as the dc supply equation: P=IV
What is the rms voltage of the mains supply?
230V
What equation links the peak-voltage to the peak-to-peak voltage?
Vpeak-to-peak = V0 x 2
V0: Peak voltage
What is a transformer?
A device that makes use of electromagnetic induction to change the size of a voltage for an alternating current
What is a transformer made up of?
An iron core with a primary coil and secondary coil
What is a magnetically soft material?
A material where its magnetisation disappears after the current is removed
How does a transformer work?
An alternating current flowing in the primary coil causes the core to magnetise, demagnetise and then remagnetise continuously in opposite directions. This produces a rapidly changing magnetic flux across the core. This passes through to the secondary coil where it induces an alternating voltage in the secondary coil. This alternating voltage has the same frequency, but different voltage if the number of turns are different
For transformers, what is the equation for the voltage in the primary coil?
Vp = Np (ΔΦ / Δt)
Vp: Voltage across primary coil
Np: Number of turns of primary coil
ΔΦ: Rate of change of flux
Δt: Change in time
For transformers, what is the equation for the voltage in the secondary coil?
Vs = Ns (ΔΦ / Δt)
Vs: Voltage across secondary coil
Ns: Number of turns of secondary coil
ΔΦ: Rate of change of flux
Δt: Change in time
What would be an ideal transformer?
Where the flux through the secondary coil is the same as the flux through the primary coil, and no energy is lost in the transfer
What is the equation for transformers, that you get from combining the equations for the voltage in the secondary coil and voltage in the primary coil?
Ns / Np = Vs / Vp
Ns: Number of turns of secondary coil
Np: Number of turns of primary coil
Vs: Voltage across secondary coil
Vp: Voltage across primary coil
What is a step-up transformer?
A transformer that has more turns on the secondary coil compared to the primary coil, so therefore increases the voltage
What is a step-down transformer?
A transformer that has fewer turns on the secondary coil compared to the primary coil, so therefore reduces the voltage
What is the main loss of energy in transformers?
Heat energy
What is an eddy current?
A looping current induced by the changing magnetic flux in the core of a transformer
Why do transformers heat up?
The metallic core is being cut by the continuously changing flux, which induces an e.m.f. in the core. The causes eddy currents, which cause it to heat up and lose energy
What does the word ‘eddy’ mean in eddy currents?
It means circular, so a circular current
How do eddy currents reduce the field strength?
They create a magnetic field that acts against the field that induced them, reducing the field strength
How can you reduce the effects of eddy currents?
By laminating the core
How does laminating the core reduce the effects of eddy currents?
It involves having layers of the core separated out by thin layers of insulator, meaning current can’t flow
Apart from eddy currents, how else is heat generated in transformers?
By resistance in the coils
How can you reduce the heat loss by resistance in the coils of a transformer?
Use wires with a low resistance - such as thick copper wires
Why are thick copper wires used in most transformers?
They have a large diameter and a small resistivity - meaning they have a smaller resistance
Apart from eddy currents and resistance in the coils, how else is energy wasted as heat in a transformer?
Energy is needed to magnetise and demagnetise the core, and this causes the core to heat up
How do you reduce the effect of heat loss due to the energy needed to magnetise and demagnetise the core in a tranformer?
You can use a magnetically soft material, which means that magnetises and demagnetises easier
What is the ideal transformer equation?
IpVp = IsVs
Ip: Current in primary coil
Is: Current in secondary coil
Vp: Voltage in primary coil
Vs: Voltage in secondary coil
For an ideal transformer, what can be said about the power?
Power in = Power out
What happen in an ideal transformer in terms of magnetic flux?
All the magnetic flux created by the primary coil would cut through the secondary coil (but in practice this never happens, especially if both coils are far apart)
How do you reduce magnetic loss when designing a transformer?
Have a core design where the coils are as close as possible
What is the equation for the efficiency of a transformer?
efficiency = IsVs / IpVp (then multiply by 100 to have as a percentage)
Is: Current in secondary coil
Vs: Voltage in secondary coil
Ip: Current in primary coil
Vp: Voltage in primary coil
How do you derive the equation for the efficiency of a transformer?
Because not all power is transferred, you calculate the ratio of power in to power out and P=IV
What is the equation for the energy lost, mostly due to heat, in a transformer?
E = Pt
E: Energy lost
P: Power
t: Time
How do you convert a transformer efficiency percentage into the power wasted?
Find the power lost by doing 100-transformer efficiency. The divide this number by 100 to get a decimal and then multiply by IpVp (which is the power in)
In the National Grid, describe the current of the electricity that is sent all around the country
It is the lowest possible current to reduce heat loss to the surroundings. Also, since P=IV, a low current means a high voltage for the same power transmitted
Why are step-up transformers used in the National Grid?
They allow us to step-up the the voltage to around 400,000V for transmission through the National Grid (meaning a lot less energy loss compared to if 230V was transmitted)
Why are step-down transformers used in the National Grid?
It’s not safe to have 400,000V use in houses, so the voltage is stepped back to a safer 230V
How do you set up the experiment for investigating the relationship between the number of turns and the voltages across the coils of a transformer?
Put 2 C-cores together and wrap a wire around each to make the coils. Start with 5 coils in the primary coil and 10 coils in the secondary coil. Set up a low voltage AC supply to the primary coil, and set up a voltmeter in parallel. Attach a voltmeter and resistor in parallel to secondary coil
How do you do the experiment for investigating the relationship between the number of turns and the voltages across the coils of a transformer?
Turn on the AC supply to the primary coil, and record the voltage across each coil. Keep Vp the same, repeat the experiment with different ratios of turns
What should you find out in the experiment for investigating the relationship between the number of turns and the voltages across the coils of a transformer?
If you divide Ns by Np and divide Vs by Vp, you should find for each ratio of turns Ns/Np = Vs/Vp
(won’t quite be the same because real transformers aren’t 100% efficient)
For the experiment to investigate the relationship between the number of turns and the voltages across the coils of a transformer, why do you use a low voltage power supply attached to the primary coil
Because transformers can increase the voltage, using a low voltage power supply keeps the voltage at a safe level
How do you set up the experiment for investigating the relationship between current and voltage of the transformer coils for a given number of turns?
Put 2 C-cores together and wrap a wire around each to make the coils. Start with 5 coils in the primary coil and 10 coils in the secondary coil. Set up a low voltage AC supply to the primary coil, and set up a voltmeter in parallel and a variable resistor. Attach a voltmeter and resistor in parallel to secondary coil. Attach an ammeter to both coils in series
How do you do the experiment for investigating the relationship between current and voltage of the transformer coils for a given number of turns?
Turn on the power supply and record the current through and voltage across each coil. Then, leaving the number of turns constant, adjust the variable resistor to change the input current. Record the current and voltage for each coil, then repeat the process for a range of current inputs
What should you find out in experiment for investigating the relationship between current and voltage of the transformer coils for a given number of turns?
Should find that Ns/Np = Vs/Vp = Ip/Is
won’t quite be the same because real transformers aren’t 100% efficient
