Chapter 23 mganric Fields

Question 1

What direction does the direction of the arrow tell you?

Answer 1

The direction a free North Pole would move!

Question 2

What happens when there is current in a wire?

What mean by current

What is the direction of the MAGENTIC field , how to determine?

Answer 2

There is a MAGENTIC field around it, with concentric circled coming out , obviously stringer closer to the wire

IMPORTSNT to note this not because of electrons but rather CURRENT

, use right hand rule, where thump points in the direction of the CONVENTIONAL CURRENT to find the direction of the MAGENTIC field

Question 3

What happens when two fields of ANY TYPE interact (are placed in the presence of each other)

Thus what happens when you put a current carrying wire in a MAGENTIC field

Answer 3

This causes a resultant force to be felt on BOTH OBJECTS CSUSIJG THE FIELD, and this force is equal in magnitude but opposite in direction acting on both, a Newtonian pair of forces

Question 4

What about the field direction for a solenoid?

Where does thump point?

Answer 4

A solenoid is a collection of wires wrapped around something . When current passed through, a MAGENTIC field is created around it which is the same as a bar magent.

The magnetic field created INSIDE THE SOLENOID is uniform and the thump points in the direction of this field

The fingers curl around in the direction of the conventional current

Question 5

What does “direction of the field mean”

Fir a solenoid

Answer 5

Direction of the field means the direction the ARROW IS POINTING IM inside the core

This is usually south to north, such thst normally your thump is pointing north

The field in the centre of the so,Enid is UNIFORMM

Question 6

Remember the IMPORTSNT bit about right hand thump rule for solenoids ?

Answer 6

They point in the direction of the MAGENTIC field ISNIDE THE CIRE

Question 7

So what can we conclude for where the thump points in a solenoid?

Answer 7

It points in the direction of the direly, so the arrow

And wherever the thumpmpoints, that ends up being the MAGENTIC NEOTH for thr solenoid / coil

Question 8

What are the conditions for a force to be felt by a current carrying wire?

Thus what is the equation, and what is defined for theta

Answer 8

It must have a COMPONENT perpendicular to the MAGENTIC field !

If it’s parallel to the MAGENTIC field it will not have a component and thus no force is felt

Equation for force is f = BILSINTHETA, where theta is the angle between the direction of the MAGENTIC field and the direction of the wire

Sin theta, because this gives you the PERPENDICULAR COMPONENT!

Question 9

What is B in the equation for MAGENTIC force

Answer 9

B is the MAGENTIC field strentgh, known as ,agentic FLUX DENSITY

This is measured in teslas!

Question 10

What is the l in the equation f = BILSINTHETA

Answer 10

L IS THE LENGTH OF THR WIRE inside the magnetic field, everything else discarded

Question 11

How to find out the MAGENTIC flux form experiment using balance in a lab

Answer 11

Use the mass scale to determine the force of the MAGENTIC field due to the current and length in wire assuming perpendicular

Crank up current to get different values

This is because as the MAGENTIC field exerts a force on the wire, an equal and oppsite firce is edged downwards on to the magents, which is picked up by the scale.

Rearrange ti find B

Question 12

Why does any charge particle movijg throught a MAGENTIC field experiences a resultant force?

Answer 12

Any charged particle means there is a rate of flow of charge means there’s current

When anytime current produced produces a MAGENTIC field of its own, which will thus interact with the present MAGENTIC field leading to a resultant force being felt

Thus it can be protons ions anything electrons, as long as you ensure it’s CONVENTIONAL CURRENT

Question 13

Why does a beam of electrons experience circular motion in the presence of a constsnt MAGENTIC field?

Answer 13

This is because the current will ALWAYS BE perpendicular to the MAGENTIC field, as it’d on an axis. Even when they change direction, they still perpendicular to the mag field , so perpendicular force still felt

Thus a perpendicular force to the velocity vector of the beam will always be felt

And whenever there is a constsnt perpendicular force to the velocity vector if anything, that body experiences CIRCULAR MOTION, where the firce points in the direction of centre of rortwiton

Thus this force = MV2 R

Question 14

How to derrive equatuon for the force felt by any charge carrier in the presence of a magnetic field when the V is known

Answer 14

In time t it will travel v t didtance

Replace this with l

And the total current = total charge / time

This means f = BQV

Question 15

When they just say electron, what ti do in F=BQV equation

Answer 15

Take Q as elementary charge

If they ask for accelrwtion take it as F/M of electron

Question 16

How to derrive the radius that the electron will travel when due it exhibiting circular motion in the presence of a constant MAGENTIC field

Answer 16

Equate BQV = MV2/R

Question 17

What happens in a velocity selector and how is velocity selected?

Answer 17

Velocity selector yiu have your beam of electrons going straight, they enter an electric field caused by two plates and a MAGENTIC field externally

These create two forces, a magnetic field one way and an electric field the other way

Although The electric force EQ is constant , based on the velocity the MAGENTIC force felt can change (BQV)

Thus only when the forces are equal, will the particle be able to escape through the other end, as these would cancel out, else one would be deflected due to an imbalance of forces

• this only occurs when E=BV, and v=E/B, so thus in this system, a range of particles can enter at different velocities,

But only thr one travel,int at THAT VELOCITY will be able to escape, and thus the velocity is guaranteed and SELECTED!

Question 18

How does a mass spectrometer work in differentiating different particles in terms of their mass only

Answer 18

First they are ionised so that they have the same charge

Then they are passed through a velocity selector , so that any ions emerging are of the SAME VELOCOTY

Now they pass through a MAGNETIC FIELD , and thus experience circular motion

• since v, B and Q are constant, the radius of curvature is proportional to their MASS ALONE

=== different weight of particles will have different radius and arrive at a detector in different places. This can then pick up the amount of abundances each weight isotope had etc…

Question 19

Even in a regular bar magnet , how do the field lines look INSIDE THE MAGNET

Answer 19

Straight uniform line,s resembles inside rhe core of a solenoid

Question 20

Okay so we know a current carrying wire which is perpendicular to a MAGENTIC field will produce a force, but can we use a force to produce a current in a wire?

Answer 20

Yes, if a force is exerted so a current carrying wire moves with some perpendicular component , then an EMF is produced in the wire

Question 21

How do we determine the DIRECTION OF CONVENTIONAL CURRENT , when you move a conductor perpendicular to a MAGENTIC field

Answer 21

Use RIGHT HAND RULE THIS TIME, same fingers and it will tell you

Question 22

Why do the electrons move when you pick up a wire in a mag field, what’s happening

Answer 22

Relative motion of the electrons to the magent, the electrons are MOVIJGZ WHEN YOU PICK THEM UP.

So imagine picking one electron upwards, it can be though of it having current upwards

Use Fleming left hand rule and you’ll see the electrons now experience a force in a direction. This is equal to BEV where v the velocity you picked them up at

• now with all the electrons experiencing a force and moving, this creates a current and thus emf!!

Question 23

How is energy conserved when electromagnetic induction occurs

Answer 23

Energy used to cause the motion is pretty much transferred to electrical energy of the electrons

Question 24

What is flux , flux density and flux linkage

Answer 24

Flux density is the MAGENTIC field stentgh B

Now just like density x volume = mass, flux density x area = flux

But need to take into account the perpendicular flux lines going into an area

So where theta is the angle to the normal

Flux = BACOSTHETA

3) flux linkage is the total amount if flux due ti coils, so 2 coils will have twice the flux bevause twice the are

So flux linkage = N x flux = BANCOSTHETA

Question 25

So when exactly is an emf produced and thus what vairbakes can we always change that will produce an emf

Answer 25

Emf is produced when there is a CHANGE IN FLUX LINKAGE
If n is 1, then change in flux

Thus if you change B,A,N, or theta, you will induce an emf

Question 26

What is lenzs law

What conservation does this adhere too?

Answer 26

When an emf is produced in a circuit it’s direction will always be such a way as to OPPOSE THE CHANGE THAT ORIGINNSLY MADE THE EMF A

this is a testament to the CONSERVATION OF PRINCIPLE OF ENERGY

Question 27

Explain lens’s law with a motor , where you’re moving a wire upwards and MAGENTIC field runs left to right

Answer 27

• moving a wire upwards, with field left to right , by right hand rule current will move TOWARDS YOU
• well now you have a CURRENT CARRYING WIRE, and this will produce its own MAGENTIC field no? Thus a force exerted?
• this force exerted by Fleming left hand rule will be DOWNWARDS,

What was the change causing the emf to be produced? A force
- and now the direction of the current produced is in such a way that it produced a force OPPOSING THE ORIGINAL

This means that you have to do work AGAINST ITS OWN FORCE, and this way you don’t violate principle of energy. The work done against is = to the electrical energy

Question 28

So how can we conclude that energy conserved when producing electric? How is it

What if there was no opposing force

Answer 28

Work is done against the force created due ti lens’s law, so energy is conserved

If there was no opposing force, then you would be able to generate electricity for free, and in fact it would be easier to, so this can’t be allowe,

Question 29

What happens when you drop a permanent magnet in a Solenoid

1) when it enters
2) once it’s in, it’s speed?
3) crossing half way

Summary = what happens to the polarity and emf directions, and speed throughout the journey

Answer 29

Letting it fall under its own weight it moves into the magnet
- as it approaches magnet, the solenoid experiences a change in flux and so emf is induced in the coil
- it is induced in a direction by lenzest law to oppose the change, so it must produce a field opposite to incoming,
- therefore the TOP PART OF THE COIL BECOMES NORTH , and bottom south, so that it can repel the magnet coming In

Once in
- the opposing force produced will be equal to the force driving magnet in
- the force driving magnet in = ti it’s own weight
- thus the opposing force will be = to own weight and the magnet inside will experience TERMINAL VELOCITY, the degree of this velocity depends on the height dropped at

AT HALF WAY
- once it crosses half way, the magnet is actually beginning to “leave” the solenoid, and so the rate of change of flux is negative
- as a result negative emf is produced this time, so On a graph this flips
- emf direction is to oppose the change . As the change is DECREASING MAGNETIC FLUX, the emf will produce a field in the SAME DIRECTION as the permanent magnet
- thus the bottom will now be NORTH and top south, so that it attracts the magnet instead, and the work done against this attraction is converted to electrical energy

So half way in between it flips direction of polarity and emf

Summary
- polarity Switches half way as the magnet transitions from entering to leaving
- this because emf switched directions half way to oppose the change producing it by lens’s law
- speed hits terminal velocity once inside as the opposing force is = to its weight

Question 30

When you drop mamgnet into a solenoid, why does dropping from higher mean it produced a HIGHER EMF, and exits in LESS TIME?

Answer 30

Recall that once inside ti goes terminal velocity
- so whatver velocity it was entering the solenoid, it remains that throughout
- thus dropping from higher gives more time for it to acclerate to a higher speed under gravity

= thus if higher velocity inside, it will escape in QUICKER TIME

2) higher emf because in faraday equation, the change in time is REDUCED, although everything else the same, this leads to a HIGHER EMF INDUCED

Question 31

Importsnt to note, what variables can acc lead to an increased emf? What’s the hidden one

IMPORTANT

Answer 31

We know emf = change in flux linkage / change in time
Thus standard BANCOSTHETA N

But also the CHANGE IN TIME, if this happens faster then HIGHER EMF INDUCED

Question 32

IMPORTSNT , if the emf to be produced in a wire is NOT PART OF A COMPLETE CIRCUIT, WHAR HAPPENS

Answer 32

NO EMF IS INDUCED

Question 33

When you bring a COIL OF WIRE into a magnetic field, when and why is emf produced

Answer 33

1) as it’s bringing in emf is induced, as there is a change of flux (the area increases)
2) once’s it’s fully in the magnetic field, if moving at a constant velocity
There is NO emf produced because no change in flux

3) While it’s leaving, it’s eexpeicnijgns decrease in flux, so change , so emf is produced but in oppsite direction

Question 34

How would a flux against time graph look for scenario when coil is bought into permanent magentic field

And thus how will emf against time look?

Answer 34

Emf against time = differentiate the flux

1) flux increases steadily, then constant, then decreases steadily

2) taking derivative of this, CONSTSNT emf, then 0 emf, then constant but NEGATIVE EMF

Question 35

What is the area in BANCOSTHETA

Answer 35

This is the area of the coil, a cross ecru on

Hence cos theta makes and gives the perpendicular area at whatver anhle

Question 36

Explain ax generator of a rotating coil, why is emf included in both directions?

Answer 36

With constant B,N,A and f, when sponning the only thing changing is the THETA

So the flux varies with theta. Think about it, when it’s vertical , it will experience max area, so max flux linkage , when its parallel (theta = 90) it experiences 0 flux as no area cut
- thus giverened by cos theta

So the flux linkage graph can be drawn as BAN as amplitude and against time if you put omega t in

• the emf is thus the NEGATIVE GRADIENT of this, so cos becomes a SIN GRAPH
• this tells us that at max flux , you have MIN EMF, and at min flux (but because the rate of change is max) yiu get max emf

Question 37

Important note to consider, what is the emf graoh always when differentiating rhe flux graoh, don’t forgets

Also remember if you start from min flux position, how to change equations for flux

Answer 37

Will be a - sign too, so negative grsdient due to lenzs law

2) if start at min position then it becomes BANSINTHETA

Question 38

So why does when you differenteste the graph amplitude emf change?

Answer 38

Because rhere is omega and so by chain rule this comes out (factor change) and if it’s bigger than 1, then it will be A POSITIVE STRETCH

Question 39

So what variables will increase the emf in a rotating generator

Answer 39

B, A,N, or f

F because what’s the equation for emf
= BANW SIN WT (remember w comes out from chain rule)

Thus max emf is prodptimsl to BAN and omega, and thus f

Question 40

Again don’t lack, when is there max EMF (in terms of angles/ flux) and how to remember

Answer 40

As emf is derivative, draw graohs

Max emf is when flux is 0, as that’s the greatest rate of change

Not when flux is max! In fact emf is 0 then loool

Question 41

What is the effect of increasing frequency on emf graoh

(Two transformations, why?’

Answer 41

One the peak amplitude increase, because emf = BANW SIN W T

And two the time period is SHORTER
- one way ti think about it is if f increases then you do 2Pi / 2PiF for a transformation by 1/f

Or a transformation by T, spin faster, shorter t so either way it works

DO NOT LACK I REPEAT DI NOT LACK

Question 42

Even for maths how do you know the time period of a sinusoids, graoh

Answer 42

You know normally the period is 2Pi

But whatever number is in front if the variable t, or theta, then you know it’s a stretch 1/x

If normal period is 2Pi, then stretch is 2Pi/ over the thing, so that’s the time period now

Question 43

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

Answer 43

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!

Question 44

Why can’t back emf ever equal the front emf

Answer 44

This because the frequency of rotation can never be large enough, as there will ALWAYS BE SOME RESISTANCE when it spins

Question 45

How does a transformer fully work, and what are components and why

Answer 45

Components consist of a primary coil with a AC SUPPLY, connected to an iron core which is connected to a secondary coil where the emf produced leaves

1) the primary coil provides an AC CURRENT to the iron core
- AC CURRENT must be hsed such that a CHANGING MAGNETIC FIELD is produced , as a magnetic field is produced when a conductor carries current

2) the iron core is used so that it can CARRY the changing magnetic flux which expands and collapsed rapidly over to the secondary coil

3) the fact that ac was used, means now that a changing magnetic field is used in the presence of a coil, by faraday equation , emf is induced!
- if it was DC CURRENT, then emf would be produced still but only once, as after that the magnetic flux would be CONSTANT
- so ac allows for mag flux to constantly be changing such that emf can be produced

Now what’s changed? The amount of coils. Thus the more coils or less, the more or less EMF IS PRODUCED

Question 46

What is the use of transformers in the national grid?

Answer 46

The use is that it steps the voltage up so current is stepped down, and thus less power is lost in the cables when transfering emf across huge distances due to power lost = I2R

Then the voltsge is stepped down again so that it can be used for home aplliances

Question 47

Assuming 100% effeicmt between the transfoemes, what is conserved?

Answer 47

Power is conserved
So equation I1 v1 = I2V2 is true
So I1/I2 = V2/ V1 also true

Question 48

However transformers are rarely 100% efficient. When they give you the power efficiency how to use this in the question. What stays the same

Answer 48

What stays the same is rhe VOLTAGE equation

The power is more to do with the CURRENT EQUATION, when not 100%l I1V1 equation not true!

, so efficiently = power in 2/ power in 1 x 100

So if you know the voltsged and power, use this equation to find the currents!

Question 49

3 reasons why transformers aren’t effienct always

Answer 49

1) we assume that the cables have no reistsnce, in reality there is always some energy lost here
2) we assume that no EDDY currents are produced itself in the iron core, as remember change in magnetic flux in presence of conductor = emf, so the iron core is acc a cknductor itself, unless you put some insulators in between

3) we also assume that the whole changing msgentic flux produced in the primary coil due to the ac current is carried over. This is not true in reality

Question 50

So how do we use 3 ways to maximise efficiency in the transformer?

Answer 50

1) use low resistance cables to reduce power loss (coils)
2) use a SOFT IRON CORE , as this maximises the magnetic field carried over

3) ensure the core is LAMINATED and made from iron layers with INSULATORS in Between to minimise the effect of eddy currents (as insulation)

Question 51

Finally conventional current for positive ions shall what direction is this?

Answer 51

Just think of it as the FLOW of positive charge, so if positive iojs one way, then that’s the conventional current

Question 52

What is the only things that can be used to MEASURE THE EMF going into or out of a transformer?

Answer 52

An ac Voltmeter
Multimeter on ac setting

Or an OSCILLOSCOPE!

Question 53

WHEN CAN WE USE E = BLV

Only time we can use, whats changing in faraday equation

Answer 53

This only works for when something is modelled as a SINGLE WIRE
- that’s because if it’s a single wire and being moved , then what’s changing? The AREA, from initially 0 area to whatever area it covered
- thus the change in area is the same as the LENTGH x change in displamcent
- over a change in time , this would be CONSTANT SPEED x l x B = e

Question 54

So why does the effect of moving a coil at CONSTANT v in a uniform field not induce emf?

Answer 54

It DOES, however it is induced in both ends of the coil, and these cancel out so no emf is induced once inside

Only when entering and exiting, ,as here your are changing B , rather than area

Question 55

Thus for the plane question, how is emf still induced using what assumption

Answer 55

Here assuming it’s a single wire, then the length of the plane x width is area, so use length as the wing to wing thing

As it changes area, emf constantly produced

Question 56

And if wire moved in unfiorm field at an accelerating rate?

Answer 56

Then it induces emf but not constantly, increasing rate I’d assume

Question 57

What is fundamental in each cire, flux or density?

Answer 57

FLUX NOT DENSITY
Flux is number of lines, these ALWAYS THE SAME

Question 58

And why is flux always constsnt EVERYWHERE WITHIN THE MAGNET

Answer 58

Because number of field lines created are never destroyed so everywhere in THAT MAGNET the flux is the same

Question 59

What you basically need to know for a level about flux

Answer 59

Everywhere in a given magnet will have same flux

This because flux is inherent priority if magnets thinking about the number of lines which are CONSERVED
- different places will have different density as area changes

Flux is the inherent property, not density, and for any given magent , the flux in the entire magent is the same!

But fi make the magnet BIGGER, the flux will increase, but still WITHIN THE MAGNET THE FLUX STAYS THE SAME