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Is the electric-field magnitude between the plates larger or smaller than that for the original capacitor?

User DirkZz
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1 Answer

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Answer:

The magnitude of the electric field will decrease

Step-by-step explanation:

The capacitance of a parallel plate capacitor having plate area A and plate separation d is C=ϵ0A/d.

Where ϵ0 is the permittivity of free space.

A capacitor filled with dielectric slab of dielectric constant K, will have a new capacitance C1=ϵ0kA/d

C1=K(ϵ0A/d)

C1=KC

Where C is the capacitance with no dielectric.

The new capacitance is k times the capacitance of the capacitor without dielectric slab.

This implies that the charge storing capacity of a capacitor increases k times that of the capacitor without dielectric slab.

The charge stored in the original capacitor Q=CV

The charge stored in the original capacitor after inserting dielectric Q1=C1V1

The law of conservation of energy states that the energy stored is constant:

i.e Charge stored in the original capacitor is same as charge stored after the dielectric is inserted.

Q = Q1

CV = C1V1

 CV = C1V1 -------2

We derived C1=KC. Inserting this into equation 2

CV = KCV1

V1 = (CV)/KC

V/K

This implies the voltage decreases when a dielectric is used within the plate.

The relationship between electric field and potential voltage is a linear one

V= Ed

Therefore the electric field will decrease

User AutoBotAM
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