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Unit 2

2.3 Dielectrics

2 min readโ€ขnovember 3, 2020

caroline-koffke

Caroline Koffke

peter57616

Peter Apps


2.3: Dielectrics

What are Dielectrics?

Dielectrics are insulating materials that are often used in capacitors to increase their capacitance. They help solve the problem of how to get more charge into a capacitor without having the voltage decrease.
Let's look back at the equation for capacitance from 2.2:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-RfUkNTleWeP3.PNG?alt=media&token=7c2f9b03-2852-4852-9c0c-5d1c9d44eb00
Modifying the equation to include a dielectric involves adding a new term k, which is the dielectric constant. In general, the easier a material is to polarize, the higher it's dielectric constant is. Values for common dielectrics are shown below:

Common Dielectrics:

MaterialDielectric constant k
Vacuum1
Air1.00059
Bakelite4.9
Fused Quartz3.78
Neoprene Rubber6.7
Nylon3.4
Paper3.7
Polystyrene2.56
Pyrex Glass5.6
Silicon Oil2.5
Strontium Titanate233
Teflon2.1
Water80

Data obtained from lumenlearning.com

The modified capacitance equations including k are:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-eZABdHrk4ciU.PNG?alt=media&token=9e45000e-4e4b-448e-9013-ef1d51c29877
In each of these equations, notice that if we have a vacuum, or air, between the plates in the capacitor, the equations return to the same form as we found in 2.2.

Why Does Adding a Dielectric Increase the Capacitance? ๐Ÿ˜•

Great question! It's because a dielectric becomes polarized easily. In fact, the easier the dielectric becomes polarized, the greater its k becomes. Let's look at an image to understand why the polarization helps increase the capacitance.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-fUr7bBLQFFBg.jpg?alt=media&token=d3a9968e-df49-4abe-992d-6ca1f4bd0282

Image from opentextbc.ca

In image (a), we can see that the molecules of the dielectric become polarized and align opposing the charge on the plates. This produces a layer of opposite charge on the surface of the dielectric that attracts more charge onto the plate, because of Coulomb's Law, increasing its capacitance.
Another way to understand how a dielectric increases capacitance is to look at how it changes the electric field inside the capacitor. Image (b) shows the electric field lines with a dielectric in place. Since some of the field lines end on charges in the dielectric (because the polarity of the dielectric is opposite that of the plates), the overall field between the plates is weaker than if there were a vacuum between the plates, even though the same charge is on the plates.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-IarWWqazebhs.PNG?alt=media&token=623f470f-d4dd-40fa-a8c3-5026c0daf835

Practice Question ๐Ÿ‘

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-JHI65z8WOzRF.png?alt=media&token=e0875e61-fc1b-4557-85de-6b963dca43cc

Image from collegeboard.org

Answers:

a)

  • i. Use Gauss' Law. Remember to include the k since we have a dielectric.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ljdZw0W809jH.PNG?alt=media&token=3ed9728c-a990-4c3a-9b88-5b3d6a40ca27
  • https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-HuDrBnHICqeH.PNG?alt=media&token=bd0d33a7-02a4-428a-bced-dc9043e31ed9

b)

  • i. Plug into the integral form of potential difference equation.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-HDf1c5yZE9iC.PNG?alt=media&token=6426cd7d-1df1-4303-a553-f481fea582c7
  • ii. Plug into the Capacitance equation
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-DmFCRfEJ85I0.PNG?alt=media&token=db536443-266d-4686-aea0-431155961c75

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