Induced current in an inductor

[Vibhor]

I am struggling with the concept of induced current in a circuit consisting of an inductor and how that induced current establishes back EMF .

Please see the page of the textbook attached .

There is a circuit consisting of an inductor , a series resistance (not shown) and a battery ( not shown ) .Initially when the switched is closed an increasing current I_ext starts flowing in the circuit .This enters the inductor from left in anti-clockwise direction as seen from left . An induced current I_in starts flowing in the inductor in the clockwise direction as seen from left .

I have a few questions .

1) Are there two currents I_ext and I_in flowing in the inductor ?How are the two currents flowing simultaneously in the inductor ? And what is the relationship between the two currents ?

I believe there is only one current flowing through the circuit .Same current I_ext flows through the inductor as well as other components .

2) Current flows from left to right in the inductor , so how can induced current cause positive charges to flow from right to left and develop a potential difference across the inductor ?Again , how can two currents flow in the inductor simultaneously ?

Thanks

 

[jartsa]

I am struggling with the concept of induced current in a circuit consisting of an inductor and how that induced current establishes back EMF .

Please see the page of the textbook attached .

There is a circuit consisting of an inductor , a series resistance (not shown) and a battery ( not shown ) .Initially when the switched is closed an increasing current I_ext starts flowing in the circuit .This enters the inductor from left in anti-clockwise direction as seen from left . An induced current I_in starts flowing in the inductor in the clockwise direction as seen from left .

I have a few questions .

1) Are there two currents I_ext and I_in flowing in the inductor ?How are the two currents flowing simultaneously in the inductor ? And what is the relationship between the two currents ?

I believe there is only one current flowing through the circuit .Same current I_ext flows through the inductor as well as other components .

2) Current flows from left to right in the inductor , so how can induced current cause positive charges to flow from right to left and develop a potential difference across the inductor ?Again , how can two currents flow in the inductor simultaneously ?

Thanks

The author seems to think that some charges must travel from A to B, before a potential difference appears between A and B. And that is not true.

When a magnet starts to move, an electric field pops into existence. Different parts of an electric field are at different potentials, because there's an electric field between the points.

 

[TSny]

I agree that the text's explanation in terms of two currents flowing simultaneously could be confusing. At any instant of time there is only one current at any point of the circuit. For me, it's less confusing to think in terms of an opposing emf produced by the induced electric field of the changing magnetic field.

When a wire is carrying a steady current, there is an electric field inside the wire that pushes the charge carriers along. So if the inductor is carrying a steady current, there is already an electric field inside the wire. But when the current in the inductor increases, the induced electric field (created by the changing magnetic field) is in a direction to oppose the current. The net electric field is thus reduced. The emf associated with the induced electric field is the "induced emf".

 

[Vibhor]

I agree that the text's explanation in terms of two currents flowing simultaneously could be confusing. At any instant of time there is only one current at any point of the circuit. For me, it's less confusing to think in terms of an opposing emf produced by the induced electric field of the changing magnetic field.

When a wire is carrying a steady current, there is an electric field inside the wire that pushes the charge carriers along. So if the inductor is carrying a steady current, there is already an electric field inside the wire. But when the current in the inductor increases, the induced electric field (created by the changing magnetic field) is in a direction to oppose the current. The net electric field is thus reduced. The emf associated with the induced electric field is the "induced emf".

Thank you very much .

Can we think of back EMF as a battery of variable potential difference ?

If yes , then if an ideal inductor is put across a battery(of EMF E) ,then how does current starts to flow as it would be a case of two equal and opposite EMF's in the circuit ?

My thinking is that even though it appears that E =Ldi/dt , the battery EMF would always be a bit higher than the back EMF because of resistance in the inductor coils .

Even if we assume there is no resistance in the inductor , then too the battery EMF is the cause and back EMF is its effect . The current however small it might be (negligiable) must flow through the coils first , only then we have a rate of change of current .As soon as the first electron crosses the coils , di/dt comes in picture and back EMF is established .

Please correct my reasoning .

 

[TSny]

There is no reason why the back emf should be equal to or even approximately equal to the applied emf. It all depends on the geometry of the inductor, the nature of the core of the inductor, the resistance of the circuit, and probably other factors.

Yes, in order for there to be any back emf at all, there must first be some current that is changing with time.

 

[Vibhor]

There is no reason why the back emf should be equal to or even approximately equal to the applied emf.

If we have an ideal inductor across a voltage source (as given in most textbooks ) ,applying Kirchoff's Law around the closed loop gives E = Ldi/dt . Isn't back EMF equal to applied EMF ?

 

[TSny]

If we have an ideal inductor across a voltage source (as given in most textbooks ) ,applying Kirchoff's Law around the closed loop gives E = Ldi/dt . Isn't back EMF equal to applied EMF ?

Oh. I didn't realize that you were now setting the resistance of the circuit to zero. (Superconducting wires?) I'm not sure what will happen in this odd case! If Kirchhoff's loop rule is assumed to still hold, then, yes, it does appear the back emf must equal the applied emf at each instant of time. You can easily solve E = Ldi/dt for a constant E to see how the current varies with time.

 

[Vibhor]

Ok .

The text attached in the OP states that in case of back EMF , there is a charge separation at the two terminals of the inductor coil ( just like a dc battery ) .It even compares it with motional EMF [When a rod moves perpendicular to magnetic field , opposite charges move to opposite ends] . Is that correct ?

 

[TSny]

I'm reluctant to agree with the text's description. For the motional emf where you have just a rod by itself moving through a B field, there will be a charge build-up on the ends of the rod. But, when the moving rod is part of an overall circuit (e.g., sliding along rails), you would not get any significant charge buildup on the ends of the rod. Likewise, when an inductor is part of a circuit, the emf induced by the inductor is not really due to charge buildup on the ends of the inductor. But some people might find it helpful to assign a "polarity" to the ends of the inductor to indicate the "direction" of the induced emf. But the induced emf is not due to charge building up on the ends of the inductor. The induced emf is due to the induced electric field created by the changing B field (which is due to the changing current!). That's my understanding, anyway.

 

[tech99]

I am struggling with the concept of induced current in a circuit consisting of an inductor and how that induced current establishes back EMF

This problems comes up very often on this forum. One way of understanding what is happening is to look at a mechanical analogy. Inductance is like inertia. Imagine applying a force (EMF) to a heavy mass (the inductor). According to Newton, it starts to move (there is current), and it accelerates (the current is growing). Newton also says that every action has a reaction. So the mass is pushing against you with the same force as you are pushing it (the back EMF). But if action = reaction (EMF = BEMF), does this mean that no movement can take place? No. The two are equal only when acceleration is taking place. If you understand the laws of motion, then an inductor is an exact parallel.
There is only one current, and the EMF always equals the BEMF provided the current is allowed to grow. If there is a series resistor, however, there will be a ceiling on the current, so eventually the BEMF will drop to zero and the current will be that for a resistor alone. It is just as if the heavy mass you are pushing is a boat, where it will eventually accelerate no more and you will be pushing against water resistance alone.
FInally, may I mention that all components in a circuit create opposition to current flow, and hence they all develop BEMFs, and all the BEMFs add up to the applied voltage.