[Physics] Current flow in a capacitor circuit on insertion of dielectric

capacitanceelectromagnetismelectrostatics

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Approach
1)Since a dielectric alters only the charge on the plates, i.e. The charge decreases as the dielectric moves inside the capacitor and then finally after reaching the middle position charge on plate increases.

2)Therefore current must flow from the positive end to the negative one i.e.A to B.

Are the above arguments correct?

given

CASE 1
The dielectric slab is moved through the capacitor
t=0 completely outside
at t=t1 completely inside
and at some time
t=t2 it has passed through the capacitor

CASE 2
the dielectric is simply inserted between the plates

Disclaimer not a homework question, a question from a recent exam.

Best Answer

I believe your reasoning is partially correct, there is just one point that is unclear.

You can assume that the insulating plate is a better dielectric than air. Inserting the plate, then, would increase the capacitance (the insulator polarizes i.e. polar molecules align with the field, and effectively reduces the electric force between the plates with their own contribution of electric force in the opposite direction). Since capacitance increases, the ability to store charge increases (it takes more charge to cause the same voltage across the plates of the capacitor since the electric force/electric field is weaker and the "voltage" is the electric field with distance taken out of account) and so more charge will flow onto the plates.

Given all that, a conventional current will flow from positive to negative - from A to B, just like you said. What seems slightly ambiguous to me is whether or not the insulator passes all the way through or if it is simply inserted in between the plates. If it is simply inserted, current will only flow from A to B. But if it passes straight through, then the capacitance will decrease after the half way point and extra charge difference between the plates will cause a stronger electric force/electric field, thus a higher voltage between the plates, than was originally supplied. Charge will then flow in the opposite direction - from B to A.


Note: I usually prefer to talk in electric force in my answers as opposed to electric field. This helps me remember that the "field" that everyone talks about is just the electric force, without taking the charge it acts on into account. Electric field is used because you don't know what the charge that feels a force will be, but it "muddies the waters" when talking like this because electric field doesn't sound like electric force.