Chapter 23 - Magnetic Fields

Question 1

Define a Magnetic Field and state what it can also be known as

Answer 1

“A magnetic field is a field surrounding a permanent magnet or a current-carrying conductor in which magnetic objects experience a force”

they are also known as B fields

Question 2

what are the easiest 2 ways to detect a magnetic field

Answer 2

1) use a plotting compass, the needle will deflect in the field to point towards the north pole of the magnet
2) use iron filings, they will only be attracted to the magnet and most of the filings will accumulate at the poles

Question 3

what do magnetic field lines do and state the rules of magnetic field lines

Answer 3

magnetic field lines map field patterns

• they go North to South
• equally spaced lines represent a uniform magnetic field
• closer lines represent a stronger field (occurs at poles)
• lines never cross

Question 4

what do the field lines look like for two magnet poles of N-N, N-S and a standalone magnet

Answer 4

• where there is N-N there are lines which curve outwards never crossing either other lines from that magnet or any lines from the other one
• where N-S, they are lines going directly from N to S, this is usually uniform directly between the magnets
• where it’s a standalone magnet you have lines curving round from North to South apart from the line exactly central on the North and South faces

Question 5

When is a magnetic field created

Answer 5

Any charged object that moves creates a local magnetic field

Question 6

what is the difference in magnetic field between electromagnets and permanent magnets

Answer 6

• in an electromagnet, the field is produced from the flow of electrons in the conductor, electrons are charged and moving and thus form a field
• in a permanent magnet, the electrons orbiting nuclei act as tiny magnets, these all align to give it permanent magnet properties

Question 7

what do the field lines for a CCC look like and what can we use to remember this

Answer 7

• the magnetic field lines around a current-carrying conductor are concentric circles perpendicular to the conventional current

we can use the right hand rule

• do a thumbs up with your right hand
• your thumb is conventional current
• your fingers represent the direction of the magnetic field

Question 8

how can we represent a current or field going into/out of a page

Answer 8

into a page = cross, imagine an arrow travelling away from you

out of a page = dot, imagine an arrow travelling towards you

Question 9

what does the field look like inside a solenoid and how does this form

Answer 9

• the field is uniform inside the solenoid and the field lines loop round from the north polarity end to the south polarity end
• we can work out which direction is north using a variation on the right hand rule
• your fingers are the direction of the current
• your thumb points to the north pole of the solenoid

Question 10

what is the factor on the strength of a field in a solenoid

Answer 10

• the coil density

Question 11

why does a CCC placed in an external magnetic field experience a force

Answer 11

• the CCC forms a magnetic field given by the right hand rule
• these field lines will ‘agree with’/increase the field on one side of the CCC but ‘disagree with’/decrease the field on the other side
• this means it experiences a force given by flemings left hand rule (perpendicular to the field and the current)

Question 12

what is Fleming’s left hand rule

Answer 12

• put out your left hand with your thumb, index finger and middle finger perpendicular to each other
• Mr Fleming’s Cat
• your thumb (M) represents Motion or force
• your index finger (F) represents Field Direction
• your middle finger (C) represents Conventional Current
• this allows you to work out the direction of the unknown quantity

Question 13

what is the equation for the force on a CCC in a magnetic field
explain each of the letters and give their units

Answer 13

F = BILsin(theta)

F = Force (N)
I = Current (A)
L = length of conductor in the magnetic field (m)
B = Magnetic Flux Density (Tesla) (T)
Theta = angle between the field lines and the CCC

Question 14

define magnetic flux density/ the tesla

Answer 14

B = F/ILsin(theta)
“The Magnetic Flux Density is 1T when a wire carrying a current of 1A placed perpendicular to the magnetic field, experiences a force of 1N per metre of it’s length in the field”

“magnetic flux density is the force experienced by a wire in the magnetic field divided by the product of it’s current, length and sin of angle between the field lines and conventional current in the conductor”

Question 15

what sort of quantity is Magnetic Flux Density

Answer 15

Vector, it has a magnitude and a direction

Question 16

explain the practical to determine Magnetic Flux Density

Answer 16

• set up a mass balance with a magnet placed on top (then zeroed) with a wire connected to an Ammeter and variable power supply (or cell and variable resistor), placed through it
• measure the length of wire in the magnetic field
• switch on the power supply at a low voltage (or cell with high resistance)
• record the change in mass (m) on the mass balance
• record the current
• repeat for other voltages/resistances
• plot a graph of I (on x) against m (on Y)
• draw a line of best fit and find its gradient
• do Grad/(l/g) to find B

Question 17

how does a charged particle moving in a magnetic field act similarly to a CCC and how can we analyse it

Answer 17

• a charged particle moving in a magnetic field acts in the same way as a CCC in a magnetic field
• it experiences a force
• it can be analysed using Fleming’s left hand rule
• if we use electrons, the conventional current is in the opposite direction to their motion
• if we use protons, the conventional current is in the same direction as their motion

Question 18

what is an electron deflection tube formed of

Answer 18

• a cell connected to a wire
• then an accelerating P.D.
• then into a vacuum tube where there’s a uniform magnetic field
• there’s also a screen which shows the electron path
• electrons are emitted through thermionic emission
• in the accelerating P.D. eV = 1/2mv^2

Question 19

how can we derive the F = BQV equation

Answer 19

consider a length of wire (L) in a uniform magnetic field (B)
we know the electrons in this wire will experience a force of
F = BIL
as L = Vt and I = NQ/t for N particles
we know
F = BNQVt/t
F = BNQV
so there is a force F for N particles which means

F = BQV for one particle
or
F = BeV for an electron

Question 20

what sort of path do charged particles in a uniform magnetic field travel on and what does this allow us to do

Answer 20

• they travel on a circular path where the centripetal force is the force due to the magnetic field so
  Fc = BIL = BQV
• this means we can use the circular motion equations

Question 21

what equation can we use to analyse the circular motion of charged particles in a uniform magnetic field and how to derive it

Answer 21

Fc = MV^2/r
BQV = MV^2/r
BQ = MV/r

r = MV/BQ

Question 22

what factors on the radius of a circle are there for a charged particle in a uniform magnetic field

Answer 22

• faster particles have a greater radius path
• higher mass particles have a greater radius path
• stronger fields decrease the radius of the path
• higher charged particles decrease the radius of the path

Question 23

what is a velocity selector

Answer 23

“A velocity selector is a device that uses electric and magnetic fields in order to filter or select particles of a specific velocity”

it is vital in instruments such as mass spectrometers and particle accelerators

Question 24

how does a velocity selector work and what forces act on a particle in a velocity selector

Answer 24

we have

• An electric field acting ‘down’ (E)
• A magnetic field acting into the plane (B)
• a small slit Z on the right

given it is a charged particle it has two forces acting on it, Fe (force due to the electric field) and Fb (force due to the magnetic field)
Fe = EQ (acts down if positive particle)
Fb = BQV (acts up if positive particle)

Question 25

how can we derive the equation for the velocity selector

Answer 25

if the particle is to pass through slit Z at the far side it must travel in a straight line so Fe = Fb BQV = EQ BV = E V = E/B

Question 26

what is the purpose of a mass spectrometer and what is the concept that they work off

Answer 26

- they are used to measure masses and relative concentrations of different types of ion or molecular ion - they work off the concept of the radius of a circular path taken by a charged particle in a uniform magnetic field

Question 27

what is the structure of a mass spectrometer

Answer 27

- Ion source = X-rays fired at a sample of the atoms/molecules used - accelerating P.D. - velocity selector - vacuum with a uniform magnetic field - detector - computer

Question 28

how does the mass spectrometer work and which equations show this

Answer 28

r = mv/BQ B is uniform, Q is constant from ionisation, and V is constant from velocity selector so r is directly proportional to m so the detector and computer can calculate masses of ions/molecular ions from their radius also worth remembering in the accelerating p.d. qv = 1/2mv^2

Question 29

how can you induce an emf | 3 methods

Answer 29

- use a coiled wire (with or without a core), move a magnet towards/away from it - run a simple d.c. motor in reverse - move a wire within a stationary magnetic field

Question 30

what are the key points to remember about the emf induced when moving a magnet towards or away from a wire

Answer 30

- magnet stationary = no emf - magnet moves towards coil = emf induced - magnet moves away from coil = opposite emf induced

Question 31

why does electromagnetic induction occur

Answer 31

- energy is always conserved - the work done to move the magnet towards the wire is transferred to electrical energy - this is because there is motion of the magnet relative to the coil - so the charged particles in the wire experience a force due to F = BIL - this makes them move to one side of the conductor producing an emf or a current if the circuit is complete - this gives electrical energy

Question 32

what is the equation and units for magnetic flux

Answer 32

magnetic flux = BAcos(theta) - magnetic flux = Phi - B = magnetic flux density - A = area - cos(theta) = cos(angle to the vertical) units = Weber, Wb = 1Tm^2

Question 33

what is a good analogy for flux vs flux density

Answer 33

flux = amount of grass | flux density = thickness of grass

Question 34

what is the equation and units for flux-linkage

Answer 34

``` Flux Linkage = N(phi) OR BANcos(theta) ``` units = Weber, or Weber-turns, Wb

Question 35

what is flux dependent on (apart from flux density and area) and what is a useful proportionality

Answer 35

flux depends on - the number of turns of a coil - the current in the coil so Phi is directly proportional to NI

Question 36

state Faraday's law and the equation/proportionalities that go with it

Answer 36

"The size of an induced emf is directly proportional to the rate of change of flux linkage" E is directly prop to delta(N(phi))/delta(t) E = -delta(N*Phi)/delta(t) an emf is induced when a conductor cuts through lines of flux or if there is a change in flux linkage

Question 37

what is the simple thought experiment that can be done to explain Lenz's law

Answer 37

- coiled wire forming closed loop, magnet moves towards/away from it - when the magnet moves towards the coil, current flows in one direction - when the magnet moves away from the coil, current flows in the other direction - when the magnet moves towards the coil, the end of the coil closest to the magnet (X) has the same polarity, this provides a resistive force - when the magnet moves away from the coil X has the opposite polarity to provide a resistive force - this means work is done to induce the current so conservation of energy holds

Question 38

state Lenz's law and the equation to go with it/ important bit

Answer 38

"Lenz's Law states that the direction of an induced current will be such that the flux it creates will oppose the change in flux that produced it" this is what gives the -ve sign in the Faraday's law equation

Question 39

How does an A.C. generator/motor work/its structure

Answer 39

- you have a coil within an external magnet - either you rotate the coil (generator) or provide a current (motor) - this will either induce a current (generator) or provide a force and motion (motor) - in a motor you have a split ring and brushes to keep it rotating in the same direction - in a generator you just have a smooth ring and brushes to induce an alternating current

Question 40

what are the graphs of flux linkage and emf produced

Answer 40

flux linkage = BANcos(theta) as B,A and N are constant the graph of flux linkage vs time is that of cos(theta) emf = -gradient of flux linkage-time graph (faraday's law) so the graph of emf is a sin(theta) graph

Question 41

what are the 4 ways to increase the EMF produced by an a.c. generator

Answer 41

- increase flux density (B) - increase area of coil (A) - increase number of coils (N) - decrease period of rotation

Question 42

what do transformers do and what are their structure

Answer 42

``` - transformers use EM induction to change voltages a simple transformer has: + a soft laminated iron core + primary coil + secondary coil ```

Question 43

how does a transformer work

Answer 43

1) A.C. is supplied to the primary coil 2) this induces a varying magnetic flux in the iron core 3) the secondary coil is linked by this changing flux 4) due to Faraday's law, an A.C. is induced in the secondary coil

Question 44

what is the transformer equation

Answer 44

``` Ns/Np = Vs/Vp Vp/Np = Vs/Ns ```

Question 45

what is the difference between a step-up and step-down transformer

Answer 45

- step-up = Vs>Vp = Ns>Np | - step-down = Vp>Vs = Np>Ns

Question 46

what is a general experiment that you can do to investigate transformers

Answer 46

- set up a transformer with a voltmeter over the power source (A.C.) by Vp and a voltmeter over Vs - change Np, Ns, or Vp and observe how Vs changes

Question 47

what is the equation for a 100% efficient transformer and how can energy loss be minimised

Answer 47

VpIp = VsIs i.e. power in = power out to minimise energy losses - use low resistance windings to reduce heating - use laminated cores with layers of insulation to reduce eddy currents - use soft iron

Question 48

how does the national grid work and why are high voltages used over the longer distances

Answer 48

The National Grid is the way that electricity is transported across the country, it uses step-up and step-down transformers to minimise energy loss P = I^2 R so power loss is lower where I is lower, so a much higher voltage is used

Question 49

why might the force/distance between an oppositely charged plate and sphere be half that of two spheres

Answer 49

the plate and sphere has an image that looks like the image from the two spheres cut in half/ mirror image/ symmetry

Question 50

why does a charged object moving on a circular path in a uniform magnetic field have a constant kinetic energy

Answer 50

- its velocity does not change as it does not accelerate | - because the force acting on the particle is at right angles to its motion

Question 51

why is the magnetic field strength inside a solenoid stronger than outside

Answer 51

- if you imagine the field lines for the coil then you have a row of crosses on one side and a row of dots on the other (representing wires going into/out of page) - using the right hand rule these dots/crosses combine to form field lines 'circuiting' the sets of dots/crosses in opposite directions - within the solenoid the field lines reinforce each other to lead to a stronger field - there is a slight overlap outside the solenoid where field lines travel in opposite directions leading to a weaker field

Question 52

what is an alternative way of defining magnetic flux

Answer 52

magnetic flux is equal to the product of the magnetic flux density and the area NORMAL to the field

Question 53

how can increasing the magnetic field strength over a moving conductor increase the emf induced

Answer 53

- it will increase the magnetic flux linkage given phiN = BANcos(theta) - hence due to Faraday's law, it will increase the emf induced/ is directly proportional to