Electromagnetic induction and alternating currents

[kihr]

Homework Statement

A solenoid with an iron core inside it is connected in series with a resistance to a battery. What happens to the defelction in the ammeter connected in the circuit when the iron core is suddenly removed?

Homework Equations

Inductive reactance = wL
Induced e.m.f. = - dPhi/dt

The Attempt at a Solution

Alternative 1

We take w=0 since this is a d.c. circuit. Hence inductive reactance of the solenoid = 0. Therefore removing the iron core from the solenoid has no effect on the current.

Alternative 2

When the iron core is suddenly withdrawn from inside the solenoid, an e.m.f. is induced in the solenoid to oppose the change (i.e. reduction of the magnetic field inside it). Hence a momentary increase in current will take place as the solenoid will try to retain its initial magnetic field (B=Mu n I where Mu = permeability; n= no. of turns per unit length; I = current through solenoid).

In my opinion Alternative 2 is the correct answer. I would, however, like to receive comments / views of the Forum members. Thanks.

 

[anathema]

Thank you for your post. I would like to offer my perspective on this question.

Firstly, it is important to note that the inductive reactance of a solenoid does not depend on the frequency of the current passing through it. It is solely determined by the inductance of the solenoid, which is a physical property of the solenoid. Therefore, even though the frequency is zero in a DC circuit, the inductive reactance of the solenoid will still be present.

Now, in Alternative 1, you have correctly stated that the inductive reactance of the solenoid is zero. However, this does not mean that removing the iron core will have no effect on the current. The inductance of the solenoid is also affected by the presence or absence of the iron core. When the iron core is present, the inductance of the solenoid is higher due to the higher permeability of iron compared to air. This means that when the iron core is suddenly removed, the inductance of the solenoid will decrease and hence the current will increase.

In Alternative 2, you have correctly stated that an induced EMF will be produced in the solenoid to oppose the change in the magnetic field. This is known as Lenz's Law. As a result, a momentary increase in current will occur, as you have mentioned.

In conclusion, both Alternative 1 and 2 are partially correct. The correct answer is a combination of both alternatives - removing the iron core will decrease the inductance of the solenoid, which in turn will cause an increase in current due to the induced EMF. I hope this clarifies your doubts. Thank you for your contribution to the forum.