# How is potential difference maintained in the inductor (in a simple R-C circuit) when the battery is disconnected?

My understanding

1. In the case of R-C circuit when capacitor is charged and battery is disconnected a potential difference is maintained (decreasing exponentially)because of the electric field existing between the plates and it reduces as charge transfer takes place .

2. Similarly in an inductor when increasing or decreasing current is passed through it a potential difference is maintained given by Faraday's law is . But how is it still maintained when the current is stopped.

(Please try not going too deep I use University Physics by Freedman and Young)

When you have an RC circuit with a battery and the capacitor is charged, the capacitor has a store of energy in the electric field equal to $\frac 12 CV^2$.
When the battery is disconnected that energy stored in the capacitor becomes heat as a current is passed through the resistor.
The current is generated because there is a potential difference across the plates of the capacitor.
The current decreases to zero when there is no longer an electric field ie the capacitor is totally discharged.

There is a parallel to this when you consider an inductor in that there is energy stored in the magnetic magnetic field produced by the inductor equal to $\frac 12 LI^2$.

When the battery is disconnected the current cannot collapse to zero instantaneously because that would imply that the magnetic flux linked with the capacitor would go to zero instantaneously and thus produce an infinite induced emf (Faraday).
So when you disconnect the battery there is still a current flowing in the circuit but that current is decreasing and thus there is an induced emf in opposition to the flux through the inductor decreasing.
As the current is decreasing the energy dissipated stored in the magnetic field (which depends on the current) is changed into heat in the resistor.
This continues until the magnetic field is no more when the current is zero.

• You said that current is maintained because it can have adverse effects if it isn't , but what exactly is the reason that it is flowing .In the case of capacitor the electric field and potential difference are related as $$E=-(dv)/(dr)$$. Is there any relation between magnetic field and potential difference. – varang rai Aug 27 '17 at 3:11
• If you have a resistor, a length of wire in the form of a coil (the inductor) connected together with wire and a current is passing through the circuit what will happen? The current will cause a heating effect in the circuit, That energy comes from the energy stored in the magnetic field which will decrease as time goes on. What produces the magnetic field? The current passing through the wire and so the current will decrease. If you think of the current as a flow of charged particles which have mass then you will appreciate that these particles cannot stop instantaneously. – Farcher Aug 27 '17 at 5:22
• So it is the fact that the charged particles have inertia which maintains the movement of those particles after the battery has been removed. – Farcher Aug 27 '17 at 5:22

When the potential difference is applied across the inductor the energy is stored in the form of magnetic field and the that magnetic energy can be mathematically expressed as $\frac{1}{2}LI^2$ and on the other hand the capacitor stores the energy in the form of electric field that can be given as $\frac{1}{2}CV^2$.

Thus super-ficially we can say that an inductor is just the opposite of capacitor, a pratically example to prove this the working of L-C Oscillations.