Physics Help Forum Induced current question

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 Jul 8th 2011, 05:30 AM #1 Member   Join Date: Jul 2010 Posts: 70 Induced current question https://sites.google.com/site/xtheunknown0/physics-1 "The switch, S, is initially open. When S is closed, a positive current flows through coil X. ...Describe the current flowing in coil Y as S is closed, held closed for some time, and then opened." (Heinemann, Physics 12 for VCE Units 3 & 4, 3rd edition) I know that since a circuit is completed, current will through the coil and produce a magnetic field along X. What do I next need to realise? xtheunknown0
Jul 8th 2011, 09:17 AM   #2
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Join Date: Dec 2009
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A little more happens

 Originally Posted by xtheunknown0 https://sites.google.com/site/xtheunknown0/physics-1 "The switch, S, is initially open. When S is closed, a positive current flows through coil X. ...Describe the current flowing in coil Y as S is closed, held closed for some time, and then opened." (Heinemann, Physics 12 for VCE Units 3 & 4, 3rd edition) I know that since a circuit is completed, current will through the coil and produce a magnetic field along X. What do I next need to realise? xtheunknown0
Hi,

The rod inside the coils, X & Y, should be presumed to be a permeable rod. A permeable rod carries magnetic flux very well and so when a B field is induced in coil X when the switch is first closed it will actually emanate from the X coil and enter where the Y coil is located (the other way actually, the direction of the induced B field will be entering into the top of the rod where the X coil is located and coming out of the bottom of the rod where the Y coil is located).

That may seem strange and you may ask why doesn't the field just go around coil X and not even go down where coil Y is located? The reason is because when the field is within the rod, it very much wishes to stay within that rod. So where one may normally think the field should come back out of the rod and enter the air moving around coil X, it does not. It instead will follow the length of the highly permeable rod to the end where it then has no choice but to leave the rod and then expand into the air as it moves back down to where coil X is located.

This B field is continuous and forms complete loops of magnetic flux that run inside the entire rod and move further away when located outside the rod (because air is not very permeable and the field lines do not like to be near each other without good reason, the rod is highly permeable and so the flux lines wish to collect and stay within it).

When the switch is first closed that lets a current flow in the counter-clockwise direction inside the circuit with coil X. That in turn induces a B field that expands roughly parallel to the rod in the direction of right to left; all the way down the rod. That expanding B field cuts across the windings in coil Y and when it does it creates or induces a current flow in the counter-clockwise direction in that circuit. The current is short lived though. The source that the current in the circuit with coil X is coming from is a direct source of current. Since the B field only changes when the current is changing, that only happens when the switch is either opened or closed.

So the little ammeter in the circuit with coil Y will show a deflection that indicates basically a "spike" of current has flown in that circuit (it is not really a spike, but if you are watching the ammeter it will deflect as if the current simply spiked), again in the counter-clockwise direction. The current will quickly reach some maximum value and then drop back to zero current flow in that circuit.

Then as the switch is opened, again a change in current induces a change in B, this time causing the field to collapse back onto the coil Y. This will induce a current flow in the clockwise direction within that circuit.

Some guy named Faraday found this out a long time ago, and so the event is named after him. This form of current induction from one circuit into another using a magnetic field, is known as Faraday's Law of Induction. Later in time some guy, arguably smarter than Faraday (Maxwell), came along and added a time changing portion to his mathematical function, collected three other equations together with that one and those four equations are known as Maxwell's equations. The one he added a time changing part to is now known as Faraday's Law of Induction with Maxwell's correction.

Take care,
Craig

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