Chapter 23 Magentic Fields Flashcards
With MAGENTIC fields what does the direction of the arrow tell you
What if lines are parallel
Where a free north would go to!
Means they are uniform magnetic field
When a wire carries current what happens
A MAGENTIC field is made around it
How ti find the direction of the MAGENTIC field
By using right hand rule, with thumb pointing in direction of the conegentionwl current, the fingers tell you direciton
What happens if a current carrying wire is placed in an external MAGENTIC field
What happens to both the wire AND the magnet
The fields will interest and as a result a RESULTSNT FORCE IS FELT on the wire, and the same force by newton 3rd law is equal and opposite and will be felt down wards by the magnet tok
How can you find the direction of the force felt
Using Flemings left hand rule, FBI, thumb index middle, thumb is force, index is direction of MAGENTIC field (which is north to south) and middle is direction of conventional current
What condtions must happen for this this force to be felt
Basicslly the MAGENTIC field and the current carrying wire must have a compoenent PERPENDICULAR TO EACH OTHER. If they don’t, (parallel) then there won’t be a force felt by the wire
What is the equation for MAGENTIC force thus
F = BIL SIN X
Where B is MAGENTIC flux density(strentgh if field), and x is the angle between the MAGENTIC field and the wire, so that a perpendicular component is used
How to find MAGENTIC flux density if a magnet in class using a weighing scale
With two magnets on the scale and wire travelling through them, will cause a resultant force either downwards or upwards based on direction . This wil be on the wire, so n equal and opposite force is felt on the MAGENTs
If the magnets pushed down, then the increases in weight (or mass and work out) is the force, and now you can rearrange.
However if magents lushed up, mass might go down, so find the modulus
Be clear, why will any charged particle moving through a MAGENTIC field experience a force?
Because current is the rate of flow of charge, so any charged particle moving will carry a current , and so will make its own MAGENTIC field, and this will interact with the current, and thus a resultant force is felt
When a bea, kf electrons travel through a MAGENTIC field, how will their motion be
IMPORTANT
This will be CIRCULAR
they feel a resultsnt force downwards, change direction, still fell resultsnt force perpendicular etc , speed doesn’t change, but direction does, thud circular motion
Acdlerwte towards centre
How ti derrive the equation of thr force felt by one charged particle in a magnetic field
Would be the same thing as F=BIL like before, however we just change it up
The particle will travel a length = VT inside the MAGENTIC field , so F=BIVT
The current is defined as the charge/t so F=BQVT/T
And thus F=BQV
Where the charge is normally the elementary fharge
Equation for force felt by one charged particle in a MAGENTIC field
F=BQV
If we know the equation for FORCE FELT by one charged particle, and know this charged particle is exhibiting circular motion, what can we equate !
That thr force for circular motion is rporivded by BQV
and thus MV2/r = BQV
What happens in a velocity selector and how is velocity “selected”
Velociy selector consists of a magnetic field forcing the charged particle one way and an electric field forcing it the other way . Only when the force felt from these fields are equal will there be no net force, meaning it will continue at the same velocity it was in and pass through the selector.
In this case EQ=BQV, and so E=BV, and V=E/B
Thus on,h certain velocities can pass through the selector, and this is a why you can confirm a particle is of certain gecko it’s
How do mass spectrometers use velocity selectors to work
What equations go on after it has left the vecoloty selector and what was point of velocity selector in the first place
Basically first atoms are singly ionised so they become charged but they all have the same charge.
- going through the velocity selector means the particles with a certain velocity are the only ones to escape.
- once escaped they meet a MAGENTIC field , which causes a resultsnt force perpendicularly and thus circular motion
- we said before if it exhibits circular motion, then mv2/r=BQV, and so r=mv/bq
- for same velocity(as this was selected), same mass , same MAGENTIC field and charge, the bigger mass ions will end up somewhere else on detector
- thus they can be detected and abundances measured
2) veocloty swlector ensured same velocity, so that only mass changes the radius
Okay we know current carrying wire perpendicular to MAGENTIC field will produce a force, but what about a force applied to a wire perpendicular to s MAGENTIC field?
This wil, produce a CURRENT!
What is this effect of generating electricity called and how do we determine DIRECTION OF CURRENT ?
Dynamo / generator effect
Use Fleming RIGHT HAND RULE, where thumb is direction of motion now
How you can explain the generation of “current” where is this energy coming from etc
HOW IS ENERGY CONSERVED
When you lift a current less wire say upwards perpendicular to a mangentic field , the stationary electrons in the WIRE, have a “velocity” upwards REA,TIVE to the MAGENTIC field
All,y left hand rule. This will show a FORCE on the electrons in a direction of the wire.
This force drives them, makes the electrons move, and this movement of electrons = CURRENT!
Basically energy is being transferred from the motion so that energy is conserved
What is FLUX (compared to flux density ) and FLUX LINKAGE
Flux density is the strength of the MAGENTIC field, then like normal density is mass/ volume, flux density is like flux / area , so flux = density x area
Basically flux is the FLUX DENSITY component PERPENDICULAR to the cross sectional area it’s going through
Thus when an angle is vertical, FLUX = BACOS(x)
Flux linkage is the number of coils x thr flux
Thus flux linkage = BANcos x
Again equations for flux and flux linkage
Flux = BACOS x
Flux linkage = BAN cos x
(Same thing , when N is one, it’s the same thing)
Thus how can you use ideas fo flux and flux linkage to explain when emf is produced?
So what variables change will produce an emf?
Emf is produced when there is a CHANGE IN FLUX LINKAGE
- it’s flux linkage and not flux because the number of coils just represents the overall flux multiplied. It’s actually just a change in flux
THUS changed B, A, THETA, or even N will induce an EMF in the wire
Okay so we know when emf is produced (change if MAGENTIC flux linkage)
HOW CAN WE FIND THE MAGENTIUDE OF EMF INDUCED
Using FARADAY LAW
EMF = - chnage in flux linkage / change in time
Where does - from faraday equation come from?
Proptinal it’s constant from lenzs law
What is lenz law PURE DEFINITION
The direction of induced emf or current is always such to oppose the change producing it
Explain lenz law with just a simple wire moving down inducing current , with MAGENTIC field right to left
Okay we know that by right hand Fleming the direction if current induced is towards us
- this current will now have its own mangentic field right? So thus it will induce a force according to left hand rule.
- this will be UPWARDS DIRECTION, which if we remember is against the ORIGNAL thing that INDUCED THE CURRENT
Thus the current induced was in a direction such that it opposed the change that caused it,
Reducing a force against
Explain how lenzs law is used to show how energy is conserved when generating electrocut
What if there was no opposing force
You are having to do work AGAINST FORCE AGSISNT YOU, thus this work is being converted into electrical energy and energy is conserved
- otherwise if there was no firce agsisnt you, then you could just push down minor and generate free energy = not fair
Explain what would happen if you just dropped a wire let it fall under IWM weight through a MAGENTIC field
Eventually it would come to a TERMINAL VELOCOTY, as the weight = to the force felt upwards
Explain lenz law through a magent entering a coil of wire
Entering a coil of wire causes a CHANGE in flux linkage and thus induced an EMF in the coils
- this emf will thus produce a MAGENTIC field , with an overall north and overall south
- if the magnet is going in, then emf is produced in such a direction that the north will be at the same face or entry, as this will repel the magnet and OPPOSE THE CHANGE THAT CAUSED INDUCTION (LENS LAW)
- as the magent goes past half way, the emf induced now switches direction!
- this is because this direction produces a MAGENTIC north at the BOTTOM NOW, to attract the south.
- here the reason emf is induced is because the magnet is “leaving “ the coil, so it produces emf in direction that will attract the magnet to oppose the change
Thus the direction of the current changed
So summarise quickly what happens to current as magent dropped into a coil
It originally one way with north at the top
After half way it switches other way with north at the bottom
How to tell what direction the currents are going in when the magent dropped in a coil
You know how to work out north snd south right
North looking down arrows on N point anti clockwise, South looking down point clockwise!
(Trick)
Thus now can we explain why there is a minus sign in faraday equation
Just used to show that the direction of the current is always OPPSOITE to what caused it
How to derrive faraday equation now using LENZ LAW IDEAS (for the force equation and negative sign)
Imagine a wire moves downwards by a force exerted
- it’s moved down a displacment delta S
- the firce applied down = to the opposing force felt on the wire by LENZ LAW
- we know force = BIL (SINX BUT ASSUME perpendicular )
Okay we know that emf = j/c and j = f d and c = change in time x I
So sub everything in and you get to emf = rate of change of flux
Which is similar to faraday, also takes into account number of coils (linkage) and negative sign for LEMZ LAW
Okay scenarios for a coil moving into a MAGENTIC field and out again. How does the emf/ current vary?
We know that emf is only induced with a CHANGE OF FLUX LINKAGE by faraday law
- this means if any of B, A , theta, N changes then there will be emf
- for constsnt B, N and theta, it means if there is a change if area inside the MAGENTIC field only then will there be EMF INDUCED
Okay
- here when it’s entering the area inside is increasing, thus emf is induced
- when fully is die no change in flux , so no current induced
- when leaving change if flux, so current induced again
How would flux against time graph and emf against time look like for that scenario or a coil entering a uniform MAGENTIC field
WHAT EQUATION LINKS THE GRADIENTS
Flux against time, INITALLy flux 0, then increases linearly, then stays constsnt, then decreases linearly, then 0
- as faraday emf = change of flux / change of time, the GRADIENT OF A FLUX AGAINST TIME GRAPH = to values of EMF !
- thus when gradient INITALLy 0, so is emf , when gradient positive and CONSTSNT, it means value of emf is positive and constsnt for same time ,
- when gradient 0, emf back to 0
- when gradient negative but constsnt, emf goes negative and constsnt for same time
Okay that thing about coil moving through MAGENTIC field in between no current produced is correct for a coil but not for just a wire, or like a plane
Why
So what happens when a plane cuts through earth MAGENTIC field
Basicslly when a line of wire just cuts through a MAGENTIC field, every second it’s changing its flux because it’s cutting flux, so emf produced yes
For a coil, this is true too, emf is produced, however as it’s a coil, it’s produced on BOTH ENDS, and thus emf CANCELS out (the area thing was just an analogy to help)
So with a plane cutting the earths MAGENTIC field, modelled as a single wire, it’s constantly cutting flux and thus there is a change in flux , so current will be induced in the plane = called EDDY current and thisnjus heats up the plane ( but also produce a force opposite direction to plane)
What equation should you use for modelling with a single wire? For magentiude if emf
Emf = BLV (which is same as change in area / time = flux / time)
Easier to model
Good analogy = HOW MORE TO THINK ABOUT SINGLE WIRE ETC CUTTING FLUX, question on what’s changing basicslly in faraday equation
What’s changing stil, is the AREA OF FLUX from the MAGENTIC field , this is being cut through and swept out m this was always the problem, as long as area inside the MAGENTIC field is being cut then emf is produced
For coil, this still happens but once fully inside then they cancel each other out, when entering sun exiting they dint that’s it
Just to be ABSOLUTELY CLEAR about what about area is going on when we talk about cutting fields. Is it the area of thr coil or the area of MAGENTIC flux lines being cut?
And even if not thr area of thr coil it’d thr area of thr revtangular encompass,ent= so not plane but rather whole rectangle
It’s the area of MAGENTIC FLUX LINES BEING CUT
But when the flux area exceeds area of coil, then the area of flux lines being cut = to the area of thr coil
Thus yiu can ALWAYS use BLV, as this takes into account area cut
Explain whole ac generator , in terms of flux, and when maximum current produced
A rectangular coil spins about an axis with a MAGENTIC fleury constsnt B
- here the only thing that’s changing flux wise is the PEPRENDICUKAR area cut through the fields, max when vertical and minimum when parallel
- the amount of perpendicular area is governed by cos theta, so theta, in essence , with B, A AND N constsnt, the only thing changing is theta!
Okay so to plot a graph of flux against time, we know flux = BANcos theta, but because only thing changing with time is theta, we can plot cos theta as BAN are constants
2) now we know the NEGATIVE GRADIENT IF A FLUX V TIME GRAPH = TO GRAPH FOR EMF
So differentiate negative cos theta , we get sin theta, so the graph for e,f is sin theta, and they are 90 out of phase
- drawing this shows us that maximum emf occurs at MINIMUM FLUX SO WHEN PARALLEL, and minimum emf occurs at MAXIMUM FLUX SO WHEN PERPENDICULAR
(Trig equations assuming you start from vertical, if start parallel switch them
To make an equation fi emf as a function of time? ( not needed)
E = max emf x cos (theta) = SIN(wt)
Now max emf apparently = BANw?
So e = BANw sin (WT)
In general how ti increase the emf produced by the generator
Here increase the
B
A
N
And the frequency , angular, w of the generator which is why max emf is BANw
Why is max emf BANW
Cuh when you differentiate flux equation you get emf = BANW SIN WT
So it depends on BAN and omega , thus f
What is Back e,f in the case for a motor
1) what is back emf and why created
2) what is the total emf going to the motor
3) what reduces the emf in the situation of the motor and why
4) easiest way to reduce the back emf?
IMPORTANT
So what is it not misconception you had, thst back emf and also LENZ law force necessarily has ti be equal to
1) When a current causes a force to be made, this FIRCE in turn created a current in oppsite direction, as an extension to Lenz law .
2) this goes in oppsite direction to incoming v, so total emf is power supply v - back emf
3) Now this current is proportional to BAN W in the system, but the inly thing we can change is the f .Thus the lower the f, the less BACK CURRENT EXPEREINCED, and thus total current (which is voltsge supply current - back emf) Is higher when the frequency of rotation is lowest
4) We can decrease the frewuency by increase the load on the motor
So not misconception that back emf HAS TO EQUAL FRONT, think of them as two separate things! Similarly the firce produced by lenz law is equal to firce produced but yiu do extra work against it and this is the work that is transferred to electrical energy
Talking about back emf, what would be the actual time voltsge supplied to the motor then
It would be the difference of V from the power supply and emf form back emf
V - E= z (IR) WHICH is the current gonna be supplied to the motor
Thus how to maximise the current being supplied to the motor
Why can’t the back emf ever equal to front
Just reduced the back emf, by decreasing the frequency by increasing load on motor
2)
For this you need to increase the frequency to infinity, there will always be some rotation lost due to work done ti reistance in the axel, air etc
EXPLAIN how a large back emf is produced when a current is suddenly turned off
EXPLAIN USIGN COLLAPSE TERMINOLY
And identify what variables is changing in faraday law equation
The current produces its own MAGENTIC field, when this is suddenly turned off, thr MAGENTIC field collapses in a very small change of time, so the change in flux is big snd for a small time the emf produced is HUGE
Think about it , area same but B rapidly changes
So if they ask to prove why huge emf occurs what ti say when a mag field collapses?
Change if lux occurs ( y either area or B dropping to 0)
Over a very small chnage in time
(Even if the change is small, the fact that the time is very small means the emf can be huge and dangerous too)
= huge emf
What is the purpose of transformers in national gird
As power lost by the cables is = I2R, we use transformers to step up the voltsge used across the transmitting cables so thst currents are kept maximum low, this means I2R is less and less power lost
Then when at home, we can use transformer again to step down the voltage and increase currents for our use
How does a transformer fully work
A transformer consists of a primary coil, a soft iron core and a secondary coil
1) the current in the primary coil given must be AC.
2) we know that a current in a coil will produced a MAGENTIC field, but because it is AC, it will produce a CHANGING MAGENTIC FIED
3) we need this. The soft iron core is then MAGNETISIED easily and “carries” the flux to the secondary coil
4) why Dow e need changing MAGENTIC field? By faraday equation emf only induced when change in flux, and here this is provided by change of MAGNETIC FIELD by ac .
5) thus when MAGENTIC field carried to secondary coil, by induction a current is produced
The amount produced is varied by the ratio of number of coils , as the magentkude of B, A and theta are all the same
So what is main equation for coils and emf for transformers
V1/v2 = N1/N2
Now assuming Transfomer 100% efficient , what is conserved, and thus what else equation
Power conserved, so I1V1= I2V2
Thus I1/I2= V2/V1
Vice Verca
I’m reality transformers aren’t 100% efficient, why is this 3 reasons
1)Because there is going to be some power loss due to resistance of cables
2) we assume all th MAGENTIC flux is transferred to the secondary wires
3) eddy currents are actually produced in the transformer too, heating it up
HOW TO MAKE TRANFOMERS AS EFFEICNET AS POSSOBLE 3 ways IMPORTANT
1) USE SOFT IRON CORE (max magnetisation and demagnetisation)
2) LOW RESISTANCE COILS (reduce power loss)
3) LAMINATED CORE SPLIT INTO LAYERS SEPARATED BY AN INSULATOR (reduce eddy)
Remember for emf equation, it’s the change in BANcos theta, but what if only one thing changing
Well the rest are constants, put the change thing in front of the thing that’s changing but do MULTIPLY BY THE CONSTSNTS 😭
Don’t be stulid
In the case of effeicnty for transformers what is equation if not 100%
Power by second coil/ power by first x 100
Using p= iv
REMEMBER ABOUT TRANSFORMERS
Is effeicny of power and turns to do with voltsge related?
NO
Effie fig if power is to more do with the CURRENT
The turns equation is ALWAYS TRUE
Remember that at theta =0, there will be max flux linkage , don’t assume 0?
Stupid
IMPORTSNT, what is conventional current
It’s the flow of POSITIVE charge aswell, not just other way of negative
So if positive ions causing current, that will be the coneventionwk current
Generator effect definition
Emf induced prorotinsl to rate of change of MAGNETIC FLUX LONKAGE
thus when dropping a agent in a coil, it’s a non uniform field so that’s why
COME BACK
- I think it’s wrong to say a single wire through a field uniform will continue to produced current, the flux is not changing its constant
- the plane is because the earth is not uniform, if you enter a non uniform field then this will happen
Doubke chekc
What must be used ti measure emf into or out of tranfeome
Ac voltmeter, osciilospe , or ac multimeter
How to do practical to see the effeciency of a transfomer
Connect coil to ac voltmeter and ammeter, find the power, do the same for number of turns , do this for different amount of coils and plot graph I guess
How will two paralle wires carrying current in SAME ways or OPPOSITE ways act and why!
Same = attract
Opposite relel
Take the mag field from one wire direction and use Fleming in it , and do the same for other wire and you’ll see
If really stuck remember if the fields cancel out and there is a vacuum they will attract
When a coil is in a mag field and if experienced forces due to the Fleming left hand, motor effect, why is a couple acting
What is the torque here proportional to
Because definition of couple are when two forces that are equal in magentiude but act in opposite directions to each other are separated by some perpendicular distance, such thst the resultant force is 0, but the rouletsnt moment isn’t 9 (hence not equiliborum, but cinstsnt vellcoity)
So forced act on esch side
And the torque which is the moment of the couple is propritnsk to the area !
Remember that MAGENTIC field and electric field have what motion and why
Electric = parabolic, because force is always in direction of the field regardless
MAGENTIC = circular motion bevause the fire e is always peprndicuskr to velocity vector no matter what
