Magnetic Fields Flashcards
What is a magnetic field?
A field surrounding a permanent magnet or a current-carrying conductor in which magnetic objects experience a force
How can you detect the presence of a magnetic field?
With a small plotting compass - the needle will deflect in the presence of a magnetic field
What do we use magnetic field lines for?
Mapping magnetic field patterns around magnets and current-carrying conductors
What are magnetic field patterns?
Useful visual representations that help us to interpret the direction and the strength of the magnetic fields
What is the arrow on a magnetic field line?
The direction in which a free north pole would move
What way does the arrow on a magnetic field line point?
North to south
What do equally spaced and parallel magnetic field lines represent?
A unform field
What is a uniform magnetic field?
One in which the strength of the magnetic field does not vary
When is a magnetic field stronger?
When the magnetic field lines are closer
Where is the magnetic field strongest for a bar magnet?
At the north and south poles
How can iron filings be used to reveal the magnetic field around a bar magnet?
Place a piece of paper on top of a bar magnet, and sprinkle iron filings around the piece of paper. The magnetic field induces magnetism in the filings, which line up in the magnetic field
What happens when a wire carries a current?
A magnetic field is created around the wire
What is the magnetic field around a current-carrying wire created by?
The electrons moving within the wire
What does any charged particle that moves create?
A magnetic field in the space around it
What are the magnetic field lines for a current-carrying wire?
Concentric circles centered on the wire and perpendicular to it
How can the direction of the magnetic field for a current-carrying wire be determined?
Using the right hand grip rule
How can the direction of the magnetic field for a current-carrying wire be determined?
Using the right-hand grip rule
How does the right-hand grip rule indicate the direction of the magnetic field for a current-carrying wire?
The thumb points in the direction of the conventional current, and the direction of the field is given by the direction in which the fingers curl around the wire
What do both a single coil and solenoid produce?
Noth and south poles at their opposite faces
What is the magnetic field pattern outside a solenoid similar to?
That for a bar magnet
What is the magnetic field at the center of the core of a solenoid?
Unform - parallel and equidistant magnetic field lines
What happens when a current-carrying conductor is placed in an external magnetic field?
The two fields interact just like the fields of two permanent magnets
What type of force do the two magnets experience when a current-carrying conductor is placed in an external magnetic field?
Equal and opposite forces
How can the direction of the force experienced by a current-carrying conductor placed perpendicular to an external magnetic field be determined?
Using fleming’s left-hand rule
How does Fleming’s left-hand rule indicate the direction of the force experienced by a current-carrying conductor placed perpendicular to an external magnetic field?
First finger gives the direction of the external magnetic field
Second finger gives the direction of the conventional current
Thumb gives the direction of motion (force) of the wire
When is the force experienced by a wire in an external magnetic field maximum and zero?
The force is a maximum when the wire is perpendicular to the field and zero when it is parallel to the magnetic field
What is the magnitude of the force experienced by a wire in an external magnetic field directly proportional to?
Current I
Length L of the wire in the magnetic field
Sin(theta) where theta is the angle between the magnetic field and the current direction
The strength of the magnetic field
What is the equation for the force experienced by a wire in an external magnetic field?
F = BILSin(theta)
B - magnetic flux density (strength of the field)
I - current
L - length of the wire
Theta - angle between magnetic field and current direction
What is magnetic flux density analogous to?
Electric field strength E for electric fields and gravitational field strength g for gravitational fields
What is the SI units for magnetic flux density?
Tesla (T) = 1Nm-1A-1
When is the magnetic flux density 1T?
When a wire carrying a current of 1A placed perpendicular to the magnetic field experiences a force of 1N per meter of its length
When a wire is perpendicular to the magnetic field, theta = 90 and sin(theta) = 1, what does this mean?
F = BIL and the direction of the force can be determined using Fleming’s left-hand rule
When a wire is perpendicular to the magnetic field and F=BIL, what is the equation for magnetic flux density?
B = F / IL
Is magnetic flux density a vector or scalar quanity?
Vector quantity - it has both magnitude and a direction
Describe an experiment to determine the magnetic flux density between two magnets
Place 2 magnets on a top-pan balance
Hold a stiff copper wire perpendicular to the magnetic field between the two magnet poles
Measure the length L of the wire in the magnetic field with a ruler
Using crocodile clips, connect a section of the wire in series with an ammeter and variable power supply
Zero the balance when there is no current in the wire
With a current I, the wire experiences a vertical upward force (LHR), and the magnets experience an equal downwards force (N3L) which can be calculated from the change in the mass reading using F = mg
Magnetic flux density can be determined with F / IL
What will a charged particle moving in a magnetic field experience?
A force
How can the effect of the statement ‘a charged particle moving in a magnetic field will experience a force’ be demonstrated for a beam of electrons?
Using an electron deflection tube
Explain how an electron deflection tube can demonstrate the effect of the statement ‘a charged particle moving in a magnetic field will experience a force’
The force on the beam of the electrons can be predicted using Fleming’s LHR
The beam of electrons is moving from left to right into a region of uniform magnetic field
As the electrons enter the field, they experience a downward force
The electrons change direction, but the force F on each electron always remains perpendicular to its velocity
The speed of the electrons remains unchanged because the force has no component in the direction of motion
Once out of the field, the electrons keep moving in a straight line
For electrons coming out of an electron deflection tube, how do they travel in a region of the uniform perpendicular magnetic field?
In a circular path
Why does a current-carrying wire in a magnetic field experience a force?
Because each electron moving within the wire experiences a tiny force
What is the equation for the force on each charged particle?
Force = Magnetic flux density x charge x speed
For a particle with charge e, F = Bev
How do you derive the equation F = BQv?
To find the force acting on a charged particle of charged Q at a speed v at right angles to a uniform magnetic fields of flux density B, consider a section of conductor, or a beam of charged particle. In a time, t, all the charged particles contained within a shaded (rectangular) region go through a section (line) XY. The length L of the shaded region is vt, where v is the speed of the charged particles.
Force on the conductor is given by F = BIL so F = BI(vt)
Current I is the rate of flow of charge so if there are N charged particles of charge Q in the shaded region I = NQ/t
So force acting on the conductor is F = B x NQ/t x vt = NBQv
So the force on each particle must be F = NBQv/N = BQv
For a charged particle of mass m and charge Q moving at right angles to a uniform magnetic field of flux density b, what will its path be and why?
A circular path because the force acting on it is always perpendicular to its velocity
For a charged particle of mass m and charge Q moving at right angles to a uniform magnetic field of flux density b with a circular path, what provides the centripetal force on the particle?
The centripetal force mv^2/r is provided by the magnetic force BQv
For a charged particle of mass m and charge Q moving at right angles to a uniform magnetic field of flux density b, what is the equation for the radius of its circular path and how is it derived?
BQv = mv^2/r
So r = mv/BQ
What does the equation r = mv/BQ show?
Faster moving particles travel in bigger circles (r ∝ v)
More massive (heavier) particles move in bigger circles (r ∝ m)
Stronger magnetic fields make the particles move in smaller circles (r ∝ 1/B)
Particles with greater charge move in smaller circles (r ∝ 1/Q)
What is a velocity selector?
A device that uses both electric and magnetic fields to select charged particles of specific velocity
What are some instruments which a velocity selector is a vital part of?
Mass spectrometers and some particle accelerators
What does a velocity selector consist of?
Two parallel horizontal plates connected to a power supply
What does a velocity selector consist of?
Two parallel horizontal plates connected to a power supply
How does a velocity selector work?
It consists of two parallel horizontal plates connected to a power supply, which produce a uniform electric field of strength E between the plates. A uniform magnetic field of flux density B is also applied perpendicular to the electric field. The charged particles travelling at different speeds to be sorted enter through a narrow-slit Y. The electric and magnetic fields deflect them in opposite directions - only for particles with a specific speed v will these deflections cancel so that they travel in a straight line and emerge from the second narrow slit Z
For an undeflected particle, what does electric force equal?
Magnetic force
What is the equation for the speed of a charged particle in a velocity selector?
V = E/B
How is the equation V = E/B derived?
For an undeflected particle, electric force = magnetic force so Eq = BQv, where Q is the charge on the particle
So, the speed v only depends on E and B hence V = E/B
How can you induce an emf using a coil and a magnet?
A sensitive voltmeter attached to the coil shows now reading when the coil and magnet are stationary
When the magnet is pushed towards the coil, an emf is induced across the ends of the coil, and when the magnet is pulled away a reverse emf is induced
Repeatedly pushing and pulling the magnet will induce an alternating current in the coil
How can you increase the induced emf across the ends of a coil?
By moving the magnet faster
How can you induce an emf with a simple dc electric motor?
By using a simple dc electric motor in reverse, e.g., using a falling mass to rotate the coil between the poles of the stationary magnet
How can you induce an emf with a loop of copper wire?
An emf is induced in a loop of copper wire when it is moved perpendicular to the magnetic field lines of a magnet
How can you increase the induced emf across a loop of copper wire?
By pulling the wire away from the magnetic field faster
Where does the electrical energy produced in a coil, when an emf is induced across the ends, come from?
Some of the work done to move the magnet is transferred into electrical energy
The motion of the coil (and the electrons in it) relative to the magnetic field makes the electrons move because they experience a magnetic force given by Bev - B is magnetic flux density, e is elementary charge and v is relative speed between the coil and magnet
The moving electrons constitute an electrical current within the coil, so the process has produced electrical energy
Explain the diagram used to aid the understanding of magnetic flux
A uniform magnetic field of flux density B passing through a region with cross sectional area A at an angle of theta to the normal
What can every experiment demonstrating electromagnetic induction be explained in terms of?
Magnetic flux
What is magnetic flux defined as?
The product of the component of the magnetic flux density perpendicular to the area and the cross-sectional area
What is the equation for magnetic flux?
Magnetic flux = magnetic flux density x cos(theta) x area
Φ = BAcos(theta)
What is the equation for magnetic flux when cos(theta) = 1?
Φ = BA
What is the SI unit for magnetic flux?
Weber (Wb) = Tm^2
What is magnetic flux linkage?
The product of the number of turns in the coil and the magnetic flux
What is the equation for magnetic flux linkage?
Magnetic flux linkage = number of turns in coil x Φ
Magnetic flux linkage = NΦ
What is the SI unit of magnetic flux linkage?
Weber (Wb) = Tm^2, although weber-turns is also used to distinguish it from magnetic flux
When is an emf induced in a circuit?
Whenever there is a change in the magnetic flux linking the circuit
How can an emf be induced in a circuit whenever there is a change in the magnetic flux linking it?
Since Φ - BAcos(theta), you can induce emf by changing B, A or theta
What does Faraday’s law relate magnetic flux linkage to?
The magnitude of the induced emf in conductors
What is Faraday’s law?
The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux linkage
How can Faraday’s law be written mathematically?
E ∝ Delta(NΦ)/Delta(t)
E - induced emf
Delta(NΦ) - change in magnetic flux linkage
Delta(t) - time interval
What is the equation that can be written from Faraday’s law and what is the constant of proportionality equal to?
E = - Delta(NΦ)/Delta(t)
Constant of proportionality = -1
What is Lenz’s law?
The direction of the induced emf or current is always such as to oppose the change producing it
How can you use (explaining lenz’s law)
What is the negative sign in the equation for Faraday’s Law mathematically expressing?
Lenz’s law
What can we use to explain the principles of an ac generator?
Faraday’s law
What is the equation for the flux linkage of a coil in an ac generator?
NΦ = N(BAcos(theta)) = BANcos(theta)
B - flux density
A - cross sectional area
N - number of turns of coil (number of coils of wire in large coil)
For an ac generator, as the coil rotates at a steady frequency, how does the flux linkage change with time?
The variation is referred to as sinusoidal and is caused by the changing cos(theta) factor
According to Faraday’s law, what is the equation for induced emf in an ac generator?
E = - (BANcos(theta)) / Delta(t)
What are some key points relating to the equation for induced emf in an ac generator: E = - (BANcos(theta)) / Delta(t)?
The magnitude of the gradient from the magnetic flux linkage graph against time is equal to the induced emf E
For an ac generator, what is equal to the induced emf, E?
The magnitude of the gradient from the magnetic flux linkage against time graph
For a given generator, B, A and N are all constant - what does this mean?
E ∝ - Delta(cos(theta)) / Delta(t)
For an ac generator, what is the maximum induced emf directly proportional to?
Magnetic flux density B
Cross section area A of the coil
Number of turns N
Frequency f of the rotating coil
For an ac generator, when is the induced emf E at its maximum?
When the flux linkage is 0
For an ac generator, when is the induced emf E 0?
When the flux linkage is at its maximum
What does a simple transformer consist of?
A laminated iron core, a primary (input) coil and a secondary (output) coil
How does a transformer work?
An alternating current is supplied to the primary coil, and this produces a varying magnetic flux in the soft iron core. The secondary coil, wound round the same core, is linked by this changing flux. The iron core ensures that all the magnetic flux created by the primary coil links the second coil and none is lost. According to Faraday’s law of electromagnetic induction, a varying emf is produced across the ends of the secondary coil
What is the turn-ratio equation?
Ns / Np = Vs / Vp - for an ideal transformer
S - secondary
P = primary
What is the difference between the number of turns on a step-up transformer and a step-down transformer?
A step-up transformer has more turns on the secondary than on the primary coil: Vs > Vp
A step-down transformer has fewer turns on the secondary than on the primary coil: Vs < Vp
What is an experiment to investigate transformers?
A multimeter set up to an ‘alternating voltage’ can be used to measure the input Vp and the output Vs voltages, or an oscilloscope could be used instead
Thin insulated copper wires are used to make primary and secondary coils
You can change the number of turns on one or both coils to see what happens to Vs for a fixed value of Vp and vice versa
When is a transformer 100% efficient?
When the output power from the secondary coil is equal to the input power into its primary coil
What is an equation for transformers relating current and voltage?
VsIs = VpIp —-> Ip/Is = Vs/Vp
In a step-up transformer, what is stepped up and what is stepped down?
The voltage is stepped up and the current is stepped down
In a step-up transformer, if the voltage is increased by a factor of 100, what happens to the output current?
It decreases by a factor of 100
In a step-down transformer, what is stepped down and what is stepped up?
The voltage is stepped down and the current is stepped up
How can transformers be made efficient?
By using low resistance windings to reduce power losses due to the heating effect of the current
Making a laminated core with layers of iron separated by an insulator helps to minimize currents induced in the core itself (eddy currents), so this too minimizes loses due to heating
The core is made from soft iron, which is very easy to magnetize and demagnetize - this helps improve the overall efficiency of the transformer
