Question

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Answer 1

a) If we analyse the given picture we find the three regions the first one represents a capacitor filled with dielectric material with dielectric constant k₁. We are assuming that the upper plate has a positive Q charge and the bottom place has - Q charge. So the capacitance in this region is given as

The energy stored in this capacitor is U₁

The electric field E₁ is given as

It's direction is towards the upper plate.

Now we move to region 2 which consists of a conductor as we know that the conductors allows the flow of the charge so no charge is accumulated on the plates separated by t which in turn yields to zero capacitance, zero electric field and the zero energy storage in this region.

Now we move to region three as we did in the first case we ca write the following expression for capacitance

The energy stored in this capacitor is U₂

The electric field E₂ is given as

The direction of electric field is towards the upper plate.

The electric field in region i is given by Eq. (3), in region 2 is zero and in region three is given by Eq. (6).

(b) The arrangement is equal to two capacitors having capacitance C₁ and C₂ are in series so the total capacitance C can be worked out as

Using Eqs.(2) and (4) in the above we get

c) The total energy stored in the field is given by U

Alternatively can be given as