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Magnetic Fields (Electromagnetic Induction
When there is a relative…
Magnetic Fields
Electromagnetic Induction
When there is a relative movement between a magnetic field and a conducting rod then an EMF will be induced across the ends of the conducting rod
Faraday's Law
The EMF induced across the ends of the conducting rod is proportional to the rate of change of the magnetic flux linkage of the coil to the magnetic field.
\[\epsilon=\frac{d(N\Phi)}{dt}\]
Lenz's Law
The direction of the induced EMF is in the direction so as to oppose the change that created it.
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For a wire moving through a field the flux linkage is the flux density multiplied by the area that the wire has traced out, leading to:
\[\epsilon=Bvl\]
Direction of induced EMF found using the right hand rule:
- First finger: Field
- Second finger: Current
- Thumb: Direction of Motion
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The change in flux linkage between two point in time is equal to the area under an EMF against time graph
Transformers
An alternating current is passed into the primary coil which creates an alternating magnetic field in the soft iron core
This alternating magnetic field induces an alternating EMF across the ends of the secondary coil, inducing an alternating current in the secondary coil
The relative number of turns on the two coils will determine whether the EMF (and therefore current inversely) across the primary coil is greater or smaller than the EMF across the secondary coil.
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A.C.
The current and EMF of an AC source will oscillate from a maximum to a minimum value, in phase with each other.
Root Mean Square \(I\) and \(V\)
The root mean square current of an AC supply in the square root of the average of the squared values of the current through the AC supply, over one complete cycle of the AC supply (same for potential difference)
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The peak current, \(I_{0}\), of an AC supply
The maximum value of the current through the supply over one cycle
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Oscilloscopes
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When the time base is switched on, the plot gives the variation of p.d. with time, plotted as a curve moving across the screen
When the time base is not switched on the output shows the current p.d., as a dot which will appear somewhere along the central vertical line
Magnetic field lines point in the direction that a north compass needle would point at that point in the magnetic field
A current carrying wire produces a magnetic field around itself, with field lines which move in concentric rings around each point of the wire
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A solenoid is a coil of wire with a length, through which a current can be passed
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The Force Acting on a Charge, \(q\), in a Magnetic Field of Constant Flux Density \(B\)
\[F=Bqv\]
Where \(v\) is the component velocity of the particle perpendicular to the magnetic field lines
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Magnetic Flux Density \(B\)
At a point in a magnetic field is equal to the force acting on a \(1m\) length of wire, carrying a current of \(1A\) at right angles to the flux lines of the magnetic field
Units of Tesla
\(1\,T=1\,NA^{-1}m^{-1}\)
Magnetic Flux \(\Phi\)
Is proportional to the number of magnetic flux lines passing normally through an area, \(A\)
\[\Phi=BA\]
Units of Webers
\(1T=1Wb\,m^{-2}\)
The flux linkage between a coil with \(N\) turns, whose normal is at an angle, \(\theta\) to the flux lines of a uniform magnetic field is:
\[N\Phi=NBA\cos{\theta}\]
The EMF induced across the terminals of a coil with \(N\) turns, rotating with angular frequency, \(\omega\), in a uniform magnetic field of flux density, \(B\) varies with time in the relation:
\[\epsilon=\omega NBA\sin{\omega t}\]
The force acting on a wire of length, \(l\), carrying a current, \(I\), perpendicular to the field lines of a magnetic field of flux density, \(B\)
\[F=BIl\]
Direction of forces found using the left hand rule:
- First finger: Field
- Second finger: Current (or direction of positively moving charge)
- Thumb: Force