Unit 4.5 - Electromagnetic Induction Flashcards
Induction
Cause something to happen
What is electromagnetic indication?
The phenomenon that electricity could be generated by moving a magnetic material relative to a conductor
What is used to generate electricity via electromagnetic induction?
Magnetic fields
Magnetic field strength (B)
This is a vector quantity. Its direction is that in which the North Pole of a freely-pivoted magnet points. Its magnitude is defined by B = F/Il, in which F is the force on a length l of a wire carrying a current I, placed perpendicular to the direction of the field. Unit T.
What is the model we can use to imagine a magnetic field?
A flow model
Magnetic flux unit
Wb
Magnetic flux symbol
φ
What is magnetic flux?
It described the “flow” of magnetism around a magnet or a wire carrying a current
What is the way we consider magnetic flux similar to?
The way we consider a flow of light from a lamp
How would we determine the intensity of a light source at a distance from it with a lamp?
By measuring the rate at which light energy passes through a given area and dividing this rate with the area
How do we get flux density?
Imagine an area A with a uniform magnetic field B passing through it
The total magnetic flux density passing through the area divided by the area gives us the flux density B at this point
How can we visually imagine flux density?
Judge how closely bunched up the lines of the field are
Flux density symbol
B
What is flux density, B?
The flux per m^2
Flux density (B) equation
B = φ/A
What is the total flux equation and how do we get to this?
φ = ABcostheta
B = φ/A
If this area is at an angle theta to the field then the formula is modified to only involve the perpendicular component of the flux density and becomes:
B = φ/Acostheta
Which is rearrange to calculate the total flux into the top equation
What does each turn in a coil have flowing through it?
A magnetic flux φ
Flux linkage
The total magnetic flux through a circuit
The total magnetic flux through a circuit
Flux linkage
Flux linkage symbol
N φ
N φ
Flux linkage
Flux linkage equation to learn
φ = BANcostheta
φ = BANcostheta
What does this equation calculate?
Flux linkage
What appends in a circuit if the flux linkage through the ciruit changes?
An emf is induced
When is an emf induced in a circuit?
If the flux linkage through the circuit changes
What are the ways in which the flux linkage of a circuit can be changed?
- By keeping the flux density constant and changing the area enclosed by the circuit
- By changing the flux density (B) and keeping the area enclosed by the circuit constant
- By a combination of both 1 and 2
What would be unrealistic to change in order to change flux linkage?
N
What is it called when the flux density is kept constant and the area enclosed in the circuit is changed?
Flux cutting
Flux cutting
when the flux density is kept constant and the area enclosed in the circuit is changed
What happens during flux cutting?
A conductor cuts across a magnetic field, cutting the lines of flux much as a lawnmower cuts grass
Equation for the area swept out per unit time by a conductor cutting across a magnetic field
A/t = lv
emf equation with flux cutting
emf = Blv
Equation for the flux cut through per unit time
Flux = flux linkage/t
What changes when we change the flux density in a circuit?
The flux linkage
Give 2 examples of when the flux linkage in a circuit would change
When a conductor experiences a changing magnetic field due to a changing current in a nearby wire
When a coil of wire is moved relative to a bar magnet
What is the emf induced in a conductor given by?
A statement known as Faraday’s law of electromagnetic induction
Transformers
Devices that transfer electric energy from one alternating current circuit to other circuits
What would cause the flux linkage in a circuit to change?
Transformers
Faraday’s law
The emf induced in a circuit is directly proportional to the rate of flux cutting or to the change of flux linkage through the circuit
Symbol for emf in electromagnetic induced theory
ϵ
Why do we use the symbol ϵ in electromagnetic induced theory?
To avoid confusion with the electric field E
Express Faraday’s law mathematically (explain)
emf = -rate of change of flux linkage
ϵ = dNφ
——
dt
ϵ = -BANcostheta/t
Flux linkage equation to learn
φ = BANcostheta
emf equation to learn (Faraday’s law)
ϵ = -BANcostheta/t
Explain what happens when flux linkage is changed in a circuit
emf induced = current induced = magnetic field
Describe the force in a circuit when the emf is zero
zero emf = force is zero
What does Faraday’s law give us a means of doing?
Calculating the magnitude of the induced emf
What does Lenz’s law add to Faraday’s law?
Direction of the emf
Lenz’s law
The induced emf is always such as to opposite the change (e.g - magnetic flux linkage) which is producing it
What is Lenz’s law responsible for in the emf equation?
The negative sign
What does an induced emf give rise to?
A current
Describe the magnetic field of a current given rise to by an induced emf
It acts so as to oppose the original change in magnetic flux which served to cause it
Describe Lenz’s law in terms of a the N pole of a magnet approaching the end of a solenoid
Lenz’s law tells us that in this situation, the end induced in the solenoid causes a current to flow through the circuit, and the direction of this current is such that it will oppose the change causing it. The two north poles repel so the motion is opposed.
Direction of a current that was caused by the emf induced in a solenoid
Such that it will oppose the change causing it
What’s does an emf induced in a solenoid cause to happen?
Causes a current to flow
In which direction does the current flow when removing a magnet from a solenoid?
The opposite direction to when putting it in
If Lenz’s law weren’t true, what would happen when putting a magnet in a solenoid? Why is this wrong?
The magnet would be pulled further into the solenoid and you could make free energy
(Conservation of energy disobeyed)
Describe the current when moving a magnet faster into a solenoid
Higher current
Why is the motion of a magnet damped when placed in a solenoid? Whose law is this according to?
Lenz’s law - motion of the magnet will be damped since the induced current acts to oppose the change in magnetic flux linkage that causes it this reduced the KE of the magnet and hence damps the motion.
How do we determine the direction of an induced current?
Using Fleming’s right hand rule
What’s the difference between the left hand rule and the right hand rule?
Left hand rule = motor (current causing motion)
Right hand rule = generator (motion causing current)
Difference between a motor and a generator
Motor = current causing motion
Generator = motion causing current
Area swept out by a straight conductor in 1 second
lv
How is an electric field induced inside a rod moving in an electric field?
Due to the motion of electrons along it
What happens when a rod is moving with a steady velocity perpendicular to a magnetic field?
Due to the motion of the rod through the field, free electrons in the rod experience a force F and are pushed along the rod
How is an electric field set up inside a rod moving along a magnetic field?
Due to the motion of the rod through the field, free electrons in the rod experience a force F and are pushed along the rod
What happens when, due to the motion of a rod through a magnetic field, free electrons in the rod experience a force F and are pushed along the rod ?
An electric field is set up inside the rod
What happens at equilibrium to the electrons in a rod that cause an electric field to be set up?
At equilibrium, force on an electron due to the electric field and the force on it due to the motion of the red through the magnetic field will be equal in magnitude and opposite in direction
Equation for when a rod is moving perpendicular to a magnetic field and at equilibrium, the force on an electron due to the electric field and the force on it due to the motion of the rod through the magnetic field will be equal in magnitude and opposite in direction
Ee = BeV
Equation for the emf induced in a straight conductor (+ explain)
Ee = BeV (at equilibrium, the force on an electron due to the electric field and the force on it due to the motion of the rod through the magnetic field will be equal in magnitude and opposite in direction)
E = Bv
E = ϵ/l
ϵ = Blv
Equation for the emf induced in a straight conductor
ϵ = Blvcostheta
Define the symbols in ϵ= Blv
B = flux density
lv = the area swept out by the rod each second
What happens when a linear conductor is moving at right angles to a uniform magnetic field?
An emf is induced
When is an emf induced in a linear conductor?
When it’s moving at right angles to a uniform magnetic field
Why is ϵ = Blvcostheta usually ϵ = Blv?
Cos theta = 1 since it’s usually vertical
When is an emf induced in a coil?
When its rotating at right angles to a magnetic field
What is the emf induced in a rotating coil related to?
The position of the coil
Flux density
Coil area
Angular velocity
Difference between the emf induced in a rotating coil and in a straight conductor?
The emf induced in a rotating coil is slightly more complex than that for a straight conductor
What is emf proportional to in both a rotating coil and a straight conductor?
The rate of flux cutting
What is proportional to the rate of flux cutting in both a rotating coil and a straight conductor?
emf
What is the magnitude of the induced emf in a rotating coil given by?
Faraday’s law
How will the magnitude of the induced emf in a rotating coil vary?
Sinusoidally with time as the coil rotates
What does the sinusoidal varying position of a rotating coil produce?
A sinusoidal current and this a sinusoidal emf
What does the emf induced in a rotating coil vary with?
Position
When is the emf induced in a rotating coil zero?
At positions where the coil is moving parallel to the field
When is the emf induced in a rotating coil maximum (be it positive or negative)?
As the coil cue perpendicular to the field
Which parts of a rotating coil have a magnetic field?
The parts which are perpendicular
List the factors which can effect the instantaneous emf in a rotating coil
The flux density
The area of the coil
The angular velocity of the rotation
What does a larger flux density mean in terms of flux linkage?
Larger fluctuations linkage
Theta in φ = BANcostheta
The angle between field B and the normal to the face of the coil
Describe and explain the induced emf if there’s a larger flux density
A larger flux density means a larger flux linkage
In a given time, the change in flux linkage would be greater
Therefore, from Faraday’s law, the induced emf would be greater
What does a larger area lead to in terms of flux linkage?
Larger flux linkage
What does a larger flux density lead to in terms of flux linkage?
Larger flux linkage
Describe and explain what a larger area of coil would lead to in term of emf
Larger area = larger flux linkage
In a given time, the change in flux linkage would be larger
From faraday’s law, the induced emf would therefore be greater
What would a larger angular velocity lead to in terms of flux linage?
The same change in flux linkage would happen in a smaller time
Explain what would be larger in a rotating coil if the angular velocity were larger
The induced emf would be larger and the frequency of the emf would be larger
A larger angular velocity means the same change in flux linkage would happen in a smaller time
Describe and explain the emf in a rotating coil at theta = 90 degrees
Maximum positive emf induced (arrows the other way = maximum negative emf)
Coil is flat, rate of change of area (and flux linkage) is maximum
emf = BANcostheta/t = max
Minimum flux linkage
Describe and explain the emf of a rotating coil at theta = 0 degrees
Coil is perpendicular to the field
Maximum flux linkage
Rate of change of area (and flux linkage) is minimum hence zero emf
Cos 0
1
Cos 90
0
When does a rotating coil have zero emf?
When perpendicular to the field
When does a rotating coil have maximum emf?
The vertical to the field
flux linkage of a rotating coil at 90 to the field
Minimum
Flux linkage of a coil perpendicular o the field
Maximum
Why is the emf of a rotating coil at maximum when it’s at 90 degrees to the field?
The rate of change of area (and flux linkage) is maximum
why is the emf of a rotating coil zero when perpendicular to the field?
The rate of change of area (and flux linkage) is minimum hence zero emf
Area of a trapezium
a + b/2 xh
How do we explain whether or not data is consistent with an equation without using a graph?
Calculate ratios
cm2 to m2
x10^-4
When does flux cutting not occur?
When something is perpendicular to the motion
What do we need to do if we’re getting inaccurate results with a Hall probe?
The probe may not be in the centre of the solenoid so we need to make sure it’s properly aligned and also use a hall probe with good resolution
What can happen once we have an emf due to flux cutting? Explain
The circuit is complete = current flows
What do we need to remember to do when calculating a ratio?
Say “ok within uncertainties”
Flux linkage and flux unit
Wb
