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Magnetic Fields (Induction (Lenz's Law
The direction of the induced…
Magnetic Fields
Induction
When there is a relative motion between a conducting rod an a the flux lines of a magnetic field, an emf will be induced across the ends of the conducting rod
For a Wire
Of length \(l\) (in the magnetic field), moving at velocity, \(v\), at right angles to the flux lines of a magnetic field of flux density, \(B\), the emf induced across the ends of the wire has a magnitude:
\[V=Bvl\]
The direction of the current induced (and therefore the emf) can be found by applying the right hand rule
Faraday's Law
The magnitude of the emf induced in a conductor is equal to the rate of change of the magnetic flux linkage of the conductor to the magnetic field
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This happens when a conductor cuts through magnetic flux lines. The more lines cut per second, the greater the induced emf
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Magnetic Flux Lines
Show the direction that a north compass needle would point in a magnetic field, which is the same as the direction of the force experienced by a theoretical north monopole at a point in a magnetic field.
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The magnetic field around a current carrying wire consists of a series of concentric rings around each part of the wire. The direction of the rings can be found by applying the right hand screw rule. The spacing of the rings increases moving outwards
When a wire is coiled into a solenoid, the magnetic field produced, when a current is passed through the wire resembles the magnetic field around a bar magnet
Around a bar magnetic, the magnetic field lines curl away from the north pole, around to the south pole
All magnetic field lines must either continue to infinity, or curl around to form closed loops
The Magnetic Flux Density
At a point in a magnetic field is equal to the force experienced by a \(1m\) length of wire, carrying a current of \(1A\) at right angles to the magnetic field lines, at that point in the field.
Measured in Tesla, where \(1T\equiv1NA^{-1}m^{-1}\)
The Magnetic Flux
Through an area, \(A\), in a magnetic field is related to the number of magnetic flux lines passing normally through that area.
\[\Phi=BA\]
Measured in Webers, where \(1T\equiv1Wb\,m^{-2}\)
Transformers
An alternating current is passed into the primary coil which creates an alternating magnetic field which passes through the soft iron core. The alternating magnetic field induces an alternating current in the secondary coil.
The ratio of the potential difference in the primary and secondary coils is equal to the ratio of the number of turns on the coils.
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Inefficiencies
Eddies
Small electrical currents can form in the soft iron core due to alternating magnetic field passing through it. These currents counter the magnetic flux passing through the core, and dissipate energy as heat. Use laminated core to fix
Core Retains Magnetism
This will mean work has to be done to re-magnetise the core, and will cause the magnetic flux to be inefficiently transmitted through the core. Use a magnetically soft material.
Heat Loss in Wires
Use fat wires, often typical for lower voltage end to have thicker wires
Not all Flux Passes Through Secondary Coil
Energy loss as not all flux from primary coil induces emf in secondary coil.
Use single core transformer
AC Current
An AC voltage source has a potential difference which oscillates between a maximum and a minimum value
When placed in a circuit, the current through the circuit will oscillate in phase with the potential difference of the source
Root Mean Square
Voltage or current is the square root of the average of the squared values of voltage or current over one complete cycle of the AC source.
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An oscilloscope will take a voltage input, and display the input voltage as a dot on a vertical axis. The timebase can be switched on, moving the dot horizontally, so that a wave can be seen, representing the voltage of the AC supply.
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Forces
A current carrying wire experiences a force acting at right angles to it's length, equal in magnitude to:
\[F=BIl\]
Where \(B\) is component of the magnetic flux density of the field perpendicular to the wire, \(l\) is the length of wire in the field and \(I\) is the current in the wire
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A charged particle moving with a velocity in a magnetic field experiences a force acing on it at right angles to it's velocity, with magnitude equal to:
\[F=BQv\]
Where \(Q\) is the charge of the particle, \(B\) is the magnetic flux density at that point in the field and \(v\) is the component of the velocity of the particle at a right angle to the magnetic flux lines at that point in the field
The direction of the force can be found by applying the left hand rule, with the current finger in the direction of the velocity for positive charges, and in the opposite direction for negative charges