# Confusion with flux and Lenz's law in an LC tank circuit

Below is an LC tank circuit and its V I plots: I marked the points in red on the plots.

As far as I understand, at point a the capacitor is fully charged and the current is zero. At point b the current reaches to maximum and the voltage goes to zero(point y).

1-) Can we say that at point b, the net magnetic flux through the inductor is maximum?

2-) Here is my real confusion: According to Lenz's law the inductor should create a magnetic field which opposes the magnetic field rate through it. But in this case the magnetic field already is created by the coil it is not external. So does the Lenz law apply here? What can we say about the flux created by the current and the opposing magnetic flux?

Between the point a and b the current increases. Does that mean the net flux increases? What about the opposing flux? Is that in opposite direction?

## 1 Answer

Can we say that at point b, the net magnetic flux through the inductor is maximum?

Yes

But in this case the magnetic field already is created by the coil it is not external. So does the Lenz law apply here?

Lenz Law does not state that the magnetic field should be external. In fact any change in the magnetic field will give rise to EMF which will try to oppose the change in magnetic field. This is actually how an inductor works, if the current through the inductor changes it will create a potential difference across its ends which would try to oppose the increase in current and hence increase in the magnetic flux (due to its own current) through the inductor coils or vice versa.
In fact this is what is called self inductance, that is, opposing the change in current due to its own magnetic flux. There is another type of inductance called mutual inductance which comes into play when there are two or more coils which couple their magnetic fields. In this case (in addition voltage due to self inductance) there will be additional potential difference to oppose the changing magnetic fields of the nearby coils.

• Regarding my second question: The current starts increasing and the flux starts increasing. Lets call this flux A. And now since there is increase in flux the inductor will create another flux which opposes the flux A, and lets call this opposition flux B. So is the net flux A - B ? – user1999 Oct 27 '17 at 0:54
• Yes it is, the opposite flux will be created by the induced electric field inside the inductor. – sarthak Oct 27 '17 at 6:32