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Conductor Linked with a Changing Strength Magnetic Field
Consider two coils of wire placed close to each other but electrically insulated from each other, as shown below.
One coil is connected to a battery through a simple on/off switch and the other is connected to a galvanometer.  
   
 
   
Notice that, the galvanometer shows a deflection (clockwise) when the current is switched on and anti-clockwise (of greater magnitude) when the current is switched off.  
This means that a system like this can be used to produce an a.c. supply from a d.c. source.
When the current in the left hand coil is switched on, the magnetic field "grows".  
You can imagine the lines of magnetic flux spreading out from the coil and therefore cutting through the wires of the other coil.  
However, keep in mind that these "lines" are just in our heads (or on our diagrams).  
They are a convenient way of thinking about magnetism.  
Notice also that when a steady current is flowing in the left hand coil, producing a constant strength magnetic field, there is no induced current in the other coil.  
The induced current in the right hand coil is greater when the current in the left hand coil is switched off than when it is switched on.  
This is because the rate of increase of the magnetic flux is limited by a the self induction of the left hand coil.  
That is, current induced in the left hand coil itself due to the changing magnetic field, opposes that change; another illustration of Lenz's law.  
   
It is clear from the animation above that much of the magnetic field produced by the coil on the left is not linked with the coil on the right.  
It can be considered to be wasted magnetism.  
The magnetic link between the two coils can be improved by putting both coils on a soft iron core (as shown below).
The presence of the iron both increases the strength of the magnetic field for a given current and also causes the field to "pass through" the other coil.  
We say that it increases the flux linkage with the coil on the right.  
The word "soft" here refers to the magnetic properties of iron.   
If you were hit on the head with the piece of iron, you would not consider it to be particularly soft  
When we say it is magnetically soft, we mean it is relatively easy to magnetize and de-magnetize (unlike, for example, steel and many magnetic alloys, which tend to retain their magnetism and are described as magnetically hard.  
 
The increased flux linkage means that it would not be a good idea to try to use the same galvanometer...  
   
click for animated version  
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