M6 Electromagnetism Flashcards
when calculating work done on a charge, the displacement value
must be in the direction of the force
electrostatic charge:
stationary, charged object that produces an electric field
electric field:
region in which a charge will experience a force (attraction or repulsion)
E=F/q describes…
the force on a charge within an electric field
E= -V/d describes
how potential changes with distance in a uniform electric field
charged parallel plates produce…
a uniform electric field
def of charge is
the difference between the number of protons and electrons in an object
3 electric field line conventions
- arrows of field lines point in the direction a positive charge would move
- field lines never cross
- distance between field lines represents their strength
equipotential field lines
each line represents an equal reduction in field strength and is independent of arrow direction
electric field around a proton
electric field around unlike charges
electric field around like charges
electric field around 2 parallel charged plates
one electronvolt is equal to (how much energy?)
1.6 x 10⁻¹⁹J
what is an electronvolt
an electronvolt is the energy gained by one electron as it moves across one volt
how to calculate an electronvolt
using W = qV
(multiply electron’s charge by 1V = energy in joules)
DON’T include negative sign as energy has only magnitude
Factors of 10, Prefix, Symbol Table
10 to the 3, -1, -2, -3, -6, -9, -12 (th) power
(first part of answer is image, second part is this text)
So, the object would reach the point with a potential of 3V before stopping. To determine the stopping point we should look back to the plates. They have a 12V potential across them, but our object only reaches a potential of 3V. This means it should only travel 1/4 of the 2m distance between the plates.
Therefore the object only travels 0.5m before stopping.
magnitude of a force on a charged particle in a magnetic field (formula) identify each component
Tesla is the unit for
another unit is…
magnetic flux density/magnetic field strength
1 weber per square meter (Wb/m2) = 1 tesla (T)
direction of a force on a charged particle in a magnetic field is shown using
the right hand palm rule
- thumb points in direction of motion of the positive charge
- fingers in the direction of the magnetic field
- palm is the direction of force
* for the direction of force on an electron, use your left hand!
force on a moving charge in a magnetic field will always be (PER/PAR) to its direction of travel
perpendicular (circular motion)
[direction of force in a magnetic field]
↓velocity or mass =
(reasoning?)
↑ deflection
a really light object or an object moving really slowly would be much easier to influence as it passes through a field
if
F = BQv
&
F = mv²/r
(radius of circular path)
r = mv/BQ
how to determine the direction of force on a moving charged particle in an external magnetic field?
RH Push/Palm Rule
Thumb in direction of positively charge
Fingers in direction of external magnetic field
Palm faces direction of force
Magnitude of Force on a current-carrying conductor in an external magnetic field
F = BIlsinθ
what is magnetic flux, formula, units
total number of magnetic field lines passing through a given area
measured in Webers (Wb)
magnetic flux density, units
magnetic field strength, measure of the density of magnetic field lines (B)
Faraday’s Law, formula
“induced emf is directional proportional to the rate of change of flux linkage”
flux linkage: number of field lines (within area of the coil)
change in flux linkage: change in field lines that thread the coil as the coil moves through the field
When a straight conductor moves through a MF, the charges separate. What quantity is used to measure the separation of charge?
Electromotive force!
emf is the name for potential energy difference created by separating charges. emf creates electrical potential energy by moving charges apart. Electric-motion, Electromotive!
emf unit
Volts
An emf separates charges and is characterised by the amount of energy it uses to separate each amount of charge. The greater the separation, the greater the potential difference
Lenz’s Law
An induced emf gives rise to a current that produces a magnetic field that opposes the original change in (relative motion) magnetic flux (that caused the induced emf)
Lenz’s Law and how energy is transformed
the induced current from movement
kinetic energy (relative motion) is lost and electrical energy is gained
The negative charge will accumulate to the right of the rod. Use RH Push Rule.
MF = out of the page (towards us)
Thumb = downwards (as wire is dragged downwards)
palm is now facing left HOWEVER,,, RH is used for positive charges, therefore the negative charges will be on the right side of the rod
anticlockwise
Current clockwise, magnetic south pole
The induced current has to create a magnetic field that repels the magnet, so as the reduce the relative motion. That means the induced current must create a magnetic south pole at the top of the solenoid. RH Grip Rule, thumb downwards, fingers curl clockwise
True or False
True
Right side of circuit has conventional current flowing downwards. RH Grip Rule, thumb points downwards, on left side, magnetic field is into the page, right side of wire, MF points out of the page
MF out of the page is experienced INSIDE THE ring (MF out of the page IS THREADING THE INSIDE OF THE COIL. To oppose this, the ring induces a current to produce a magnetic field into the page ON THE INSIDE OF THE COIL. RH Grip Rule for ring now. Fingers curl into the page on left side of circle, thumb points up which is clockwise current
Lenz’s Law
Bar Magnet & Solenoid
Loop & B-field
Bar magnet & solenoid
- current through the solenoid opposes change by creating a pole to attract/repel moving bar magnet
RH rule:
Thumb: North Pole
Fingers: Current
Loop & MF
- current through the loop generates opposing MF to counteract change in flux
thumb: current
Fingers: MF
the difference between Faraday’s Law and Lenz’s Law is that…
Lenz’s law includes the direction of the induced EMF
Repulsive and attractive
The magnet is moving, so the copper tube is experiencing a change in magnetic flux. This means the copper tube must induce an emf that will be directed such that it opposes the change that created it.
As magnet enters, magnetic flux through tube increases so a repulsive force is generated to slow the magnet’s approach
As magnet exits, the flux through the tube decreases so an attractive force is generated to slow the magnet’s departure.
current will flow clockwise
With the application of a MF out of the page, the loop has experienced a change in magnetic flux and will hence induce an emf by Faraday’s Law. Lenz’s Law states that this emf should be directed to oppose the change that created it, so the emf will create an MF into the page.
RH Grip Rule
Fingers curl into the page on inside of coil (AS THE EMF LINES ARE THREADING THROUGH THE COIL ON THE INSIDE OF THE LOOP) and thumb points clockwise
Constant velocity of an object means that kinetic energy is…
neither increasing nor decreasing
formula for calculating a force on a current carrying conductor in an EMF is
the acceleration of a charged particle in a uniform electric field is
constant in magnitude and direction
uniform electric fields act very similarly on objects to…
Earth’s G Field
therefore we can analyse motion in Electric Fields using projectile motion equations
draw 2 examples of uniform electric fields
compare the three vector fields (gravitational, electric, magnetic)
explain why a charge moving in a magnetic field will experience centripetal force
draw a diagram to explain
The force on a charge moving across the MF is perpendicular to its velocity (as well as MF, as seen in RH Palm rule), which causes a change in direction. This means the velocity of the charge changes, and the force direction will then change to be perpendicular to the velocity. This goes on.
anticlockwise
a magnetic field direction of into the page increased (as it went from no MF to MF), this can be visualised as bringing a north pole closer to the coil of wire. To oppose this, the coil must produce a north pole. This means the current will flow anticlockwise.
formula for 2 parallel current-carrying conductors
and same/diff current direction
same current direction: wires attracts
difference current dir: wires repel
The loop of wire will stretch outwards.
draw the magnetic field around
a single bar magnet
2 north poles close to each other
a horseshoe magnet
how to determine poles of a solenoid using N & S writing
for parallel current carrying conductors,
magnitude of force? direction of force? true even if?
magnitude of forces is equal, direction of force is opposite, true even if the conductors carry current of diff magnitudes
N3L force pair
diagrams of parallel current carrying conductors
using F = BILsinθ, DERIVE parallel current carrying conductor
B = (kI)/r
θ in sinθ is the angle between the current carrying conductor and external magnetic field (90 degrees)
subbing those values in
you get the formula kIIL/d
k = μ/4π = 2.0 x 10⁻⁷ NA⁻²
explain how the speed of the relative motion between external magentic field and conductor affects the current induced
a slow moving magnet induces a smaller current than when the magnet is fast moving
because the change in magnetic flux threading the conductor is occurring at a faster rate
magnetic flux is the name given… units, symbol
to the amount of magnetic field passing through a given area
Φ, Webers (Wb)
magnetic field strength is the same as saying
magnetic flux density
Φ =
formula explanation
BAcosθ
B is magnetic field strength
A is given area
θ is the angle between the normal of the surface of the area and the magnetic field lines
looking for the component of magnetic flux density that is perpendicular to area A
The Motor Effect (teacher def)
A current carrying conductor in an external magnetic field experiences a force
Lenz’s Law (teacher def)
*everything happens at once
An induced emf gives rise to a current that produces a magnetic field that opposes the original change in magnetic flux that caused the induced emf
Faraday’s Law of Induction
the induced emf in a circuit is equal in magnitude to the rate at which the magnetic flux through the circuit is changing with time
change in is
final - initial
what is a transformer
a device that modifies the size of the supplied voltage for an alternating current
Vₚ
Nₚ
Vₛ
Nₛ
input and output coil
voltage through primary coil
number of turns in the primary coil
voltage through the secondary coil
number of turns in the secondary coil
input coil: primary coil
output coil: secondary coil
Voltage:Turns Equation
Step Up and Step Down Transformers with voltage and turns
Function of a transformer is entirely based on the principle of…
electromagnetic induction
A transformer will not work without a soft iron core, T or F?
FALSE!
Pₚ = Pₛ
assuming 100% efficiency (no energy wasted)
IₚVₚ = IₛVₛ
step up transformers are used to increase the voltage output. why?
P = VI
if voltage is increased, current is decreased. This means less energy will be wasted to heat energy.
why are transformers used to transport power
In a power transmission system, electricity first moves from a power station to power lines, then to households. What two transformers, in order, should be used in this system?
ohmic heating
resistance in the wires of the transformer heat up due to the collisions between electrons
* minimise by increasing coil thickness
step down transformer needs thicker wires for which coil?
step up transformer needs thicker wires for which coil? why?
why do we step down multiple times in power transmission?
We step down for safety reasons. It is done over multiple steps to strike the balance between minimising power loss and maximising safety.
eddy current is the induced current (lenz’s law)
but in a flat metal sheet (iron core of a transformer). since it’s not in a wire and doesn’t have a determined direction, it just flows to reduce the change in flux that caused them
eddy currents are reduced by
laminating the iron core
the iron core is laminated with insulative layers to reduce the size of induced eddy currents, therefore minimising unwanted heat, and improve efficiency of transformer
why are eddy currents produced in the transformer?
the metal core experiences the change in flux it transmits to the secondary coil
power efficiency formula
power out / power in
Pₛ/Pₚ
In transformers, incomplete flux linkage refers to losses due to
flux from the primary coil not properly threading through the secondary coil
Transformers carry energy from one coil to the next using electromagnetic induction
eddy currents are circular currents formed in conductors when…
there is a change in flux threading the conductor
adding a load to a motor will decrease the back EMF in the motor’s coil. T or F?
T!
If we added a load to our motor, the motor would begin to rotate slower. If the motor rotated slower, the rate of change of flux in the motor’s coil would decrease. Because of this, the back EMF would decrease. So adding a load to a rotating motor would decrease the back EMF.
3 limitations of the ideal transformer model
incomplete flux linkage/ flux leakage: the magnetic field generated by the primary coil does not entirely thread through the secondary coil A MAGNETIC FIELD CAN ALWAYS BE DETECTED NEAR A TRANSFORMER
resistive heat production: the primary and secondary coils of transformers are made from thin copper wires. When a current passes through the wires they heat up, so energy (and power) are lost in the primary and secondary coils THERMAL IMAGES OF TRANSFORMERS SHOW THAT THEY HAVE HIGHER TEMPS THAN THEIR SURROUNDINGS
eddy currents in the iron core: the changing magnetic field passing through the iron core causes a force on the loosely bound electrons (EMF), creating eddy currents
turns ratio of a transformer
number of turns of primary coil vs number of turns of secondary coil
What are the 3 main functions of the brushes in a DC motor?
- to maintain electrical contact between the battery and coil
- to ensure the motor rotates smoothly
- to avoid tangling in the wires due to rotation
The brushes are smooth electrical contacts that allow the commutator to reverse the direction of current every half turn without tangling the wires.
in the diagram, which direction will the motor rotate?
It will rotate clockwise, using TME RH Push rule
which direction will the motor rotate?
anticlockwise! use TME RH Push rule and get direction of current from the battery terminal
a larger back EMF makes motor burnout more likely. T or F?
False!
a magnet is dropped from a height of 2m directly above a pure copper plate. what best describes the net force on the magnet as it falls?
the net force is decreasing
A student claims that a DC generator is “a DC motor in reverse”. Assess the validity of this claim with reference to the structure and function of a simple DC generator and DC motor. Include diagrams!
- Diagrams!
- Sim & Diff!
- both contain the same parts: an external magnetic field, a rotating coil of wire, and a split ring commutator
- motor converts electrical energy to kinetic rotating energy
- generator converts kinetic rotating energy into electrical energy
- Judgement!
So, as the structure is the same, but the function is opposite, the student’s claim that a DC generator is the reverse of a DC motor is valid.
what does a split ring commutator do in a DC motor and generator?
it inverts the direction of the current in the circuit every 180 degrees
3 differences between AC & DC generators
what is a generator?
a machine that converts mechanical energy into electrical energy by rotating a coil of wire in a fixed magnetic field
process of a generator
the continually rotating coil results in a change in magnetic flux
the changing flux induces a current in the coils, which is passed through a commutator
the output can then be used for power
atomi diagrams of DC and AC generators
what is a motor
a device that transforms electrical energy into rotational kinetic energy. the rotational energy is produced by passing a current through a coil in an external magnetic field.
electromagnetic braking with train wheels
explain process and how to find direction of eddy current
eddy current: using RH push rule
palm facing left as the wheel is rotating that way, fingers pointing into the page, thumb points upwards
wheel:
an electromagnet is switched on so an external MF affects the part of the metal wheel in the external MF and eddy currents are induced. These eddy currents inside the MF experience a force that acts in the opposite direction to the relative motion of the train wheel so the wheel is slowed down.
contrast the design of transformers and magnetic braking systems in terms of the effects that eddy currents have in these devices
part 1: Transformers
contrast the design of transformers and magnetic braking systems in terms of the effects that eddy currents have in these devices
part 1: Magnetic Braking Systems
when a change moves along a MF parallel to the field lines, what force?
it experiences no force
a motionless change in a MF experiences what force?
no force
when does F = qvBsinθ have its maximum value?
when the velocity is perpendicular to the field lines
sinθ = sin90 = 1
electric fields produce _________ trajectory WHEREAS magnetic fields produce a _______ trajectory
what is an electromagnet?
a solenoid that has a soft iron core
the strength of an electromagnet can be increased by
- increasing the current through the solenoid
- adding more turns of wire per unit length for a long solenoid
- increasing the amount of soft iron in the core
electromagnet benefit?
when a current flows through the solenoid, the iron core becomes a magnet. The polarity of the iron core is the same as the polarity of the solenoid, so the core produces a much stronger magnetic field than is produced by the solenoid alone.
what is a motor
it converts electrical energy (current) to kinetic energy (rotational motion {torque})
5 parts of a DC motor
source of emf: battery drives current through the coil
rotor -> armature: a frame on which coils are wound, coil rotates within the external MF
stator: provides the the magnets external MF: supplied by permanent or solenoids
split ring commutator: reverse current direction every 180 degrees to keep coil rotating in the one direction (to maintain constant direction of torque) by alternating contact with the brushes (connected to DC source) every half-turn
brushes: maintain electrical contact between circuit and commutator
how to increase maximum torque acting on the sides of the DC motor (to increase speed)
- increasing force acting on the sides
τ formula torque
nBIAcosθ
θ is the angle between the plane of the coil and the magnetic field
diagrams of permanent magnet and electromagnet
which expression can be used to calculate the balance reading
using
P = VI
V = IR
derive power loss equation
Power Distribution System (4 Aspects) (& which transformers?)
Power Station
- generate electricity at 23kV
Regional Substation
- receives VERY HIGH voltage transmission to reduce heat caused by high current 330-500kV
Local Substation
- receives HIGH voltage transmission 110kV
Home Sweet Home
- 240V
How does the law of conservation of energy justify Lenz’s law?
torque in a motor formula
why do DC motors need a split ring commutator?
3 advantages of AC induction motor
- rotation of squirrel cage is friction-free > less maintenance is required
- no need for brush & commutator so there are no sparks when the commutators “scrape” past the brushes > more energy efficient
- since rotational speed is controlled by electromagnets, it is more reliable
3 disadvantages of ac induction motors
- limited rotational speed > limited applications
- complex start up due to need of three phases of electromagnets
- low starting torque (rotor needs to “warm up” gradually to desired speeds)
account for the 3 “lost power” of induction motors
Power is lost in the creation of eddy currents in the iron core. These currents create heat and waste energy.
Mechanical losses occur through friction at the bearings of ends of motor
Losses of power in the resistance of the copper wiring
slip/slip speed is defined as
the difference between speed of stator magnetic field and rotor speed
explain why slip is necessary for the operation of a squirrel cage induction motor
7 steps to operating mechanism of DC motor
- current flows through the coils of motor, creative a force due to TME
- this force has a rotational effect (torque), which causes the rotational acceleration of the rotor
- as the rotor rotates, angle between point of application of force and the line joining the pivot point to point of application of force, causing torque to decrease to a minimum when coil is vertical
- to ensure torque is in the same direction (continuous rotation of rotor) a split ring commutator reverses direction of current every half turn
- as the motor spins through the EMF, the magnetic flux threading the coil changes. this induces “back emf”
- By lenz’s law, this back emf induces a current that produces a magnetic field to oppose original change in flux. It reduces the current in the coils, therefore reducing force and torque.
- as the motor speeds up, the back emf increases until a point where it equals the supply. Then, there is no net current, force or torque, and the motor has reached an equilibrium at its maximum speed: operational speed
what is a generator
a device that converts mechanical energy (kinetic) into electrical energy
AC & DC generators have same anatomy as a DC motor except for
slip ring for AC generator
split ring for DC generator
difference between DC generator and DC motor
in a DC generator, the armature is manually rotated and the output is electrical energy
conversely, in a DC motor, the input is electrical energy and this causes the armature to rotate
deriving work for W = qV
W = change in energy
= Fd
(since F for a charge is F = Eq)
W = Eqd
and since V=Ed
W = qV
although all these equations are on formula sheet… so
there are 5 different θ’s
write the 5 formulas
in, θ is the angle between
the velocity of the positively charged particle and external magnetic field
in, θ is the angle between
conventional current in wire and external magnetic field
in, θ is the angle between
plane of the coil’s surface area and external magnetic field
in, θ is the angle between
point of application of force and the line joining the pivot point to point of application of force
in, θ is the angle between
the normal of the surface of the area and the magnetic field line
what is used for
calculating the torque of a coil in a DC motor
apply lenz’s law to this scenario
emf vs time for DC generators
DC generators produce unidirectional current so all the emf is positive
DC generator’s graph is the absolute value of AC generator’s graph (all that is happening is the split ring is reversing the direction of current)
emf vs time for AC generator
the polarity of emf (pos/neg) corresponds to direction of current
AC generators produce bidrectional current. the directional alternates twice a revolution.
relationship between flux vs time graph and emf vs time graph and current vs time graph
you can think of the emf graph as the NEGATIVE gradient of the flux graph (it is if you differentiated the flux graph and then mult. by -1)
in this example, the flux graph resembles a sin wave
therefore, the emf graph resembles a negative cos wave
the emf and current graph is the same because emf is the force that moves electrons and current is the amount of charge that passes a point over time
–> the emf is creating the current
Lenz’s Law & How to determine direction of induced current 3 ways
- RH Oppose Rule
a) face palm in direction that OPPOSES incoming magnet (relative motion of EMF and conductor in that EMF)
b) point fingers in direction of EMF
c) thumb shows direction of current - LH Rule
a) face palm in direction of incoming magnet (flux lines threading through the coil)
b) point fingers in direction of EMF
c) thumb shows direction of current - RH Grip Rule
a) visualise a different perspective of diagram in question
→ instead of the conductor moving sideways into an EMF pointing into the page, IMAGINE a north pole is being moved closer to the conductor
b) point thumb in direction that a north pole should be facing to oppose change in flux lines threading the coil
c) direction of curled fingers are whether the current is anticlockwise or clockwise
right before the conductor is dropped, it has some unknown amount of GPE. most of the GPE is converted into kinetic energy, however since the conductor is moving in an EMF, it will induce an EMF to oppose changes in flux by Lenz’s Law. So some of the kinetic energy is converted to electrical energy inside the conductor as well!
ΔGPE = Eₖ + Eₑₗₑ꜀ₜᵣᵢ꜀ₐₗ
We are looking for electrical energy
ΔGPE = mgh
= 4 x 9.8 x 2
= 78.48J
Eₖ = ½mv²
= ½ x 4 x 3 x 3
= 18J
rearrange for Eₑₗₑ꜀ₜᵣᵢ꜀ₐₗ
Eₑₗₑ꜀ₜᵣᵢ꜀ₐₗ = 78.48 - 18
= 60.48J
current vs motor speed graph
a negative linear relationship
it’s to do with
total voltage = supply voltage - back emf
and eventually reaching operational speed
what does back emf cause in motors?
when total voltage is 0, the motor reaches its max velocity (operational speed) as net force on each side of coil is 0 as there is no net current
otherwise it would rotate and accelerate on forever
5 ways to reduce overheating of transformers otherwise metal could
expand and melt
be in a well-ventilated space, fans, heat sink fin to increase surface area exposure to air for heat to dissipate, submerge it in cool oil (hot oil is then pumped out, cooled, and pumped back in), pads to raise the transformer above ground,
hand drawn diagrams of ac and dc generators
Compare and Contrast Gravitational, Electric and Magnetic Fields
Similarities: all forces are directly proportional to the field strength
explain the shape of the graph
T or F
AC generators are more effective than DC generators for high current applications
It’s true! AC generators are great for high current applications. The easiest way to produce higher currents is to add multiple turns to our coil. But a coil with more turns is much heavier, so it’ll be harder to rotate. However, AC generators can be constructed so their coils are the stationary part and the magnetic field is rotating. If we aren’t moving our coil, it doesn’t matter how heavy it is! So, AC generators are fine to have larger coils to produce large currents.
