1. Dielectrics Experiment: Place dielectrics between
plates of capacitor at
Q=const condition
Observation: potential difference decreases to smaller value with
dielectric material relative to air
𝐶 0 = 𝑄 𝑉 0
Without dielectric:
because V<V0
C>C0
𝑄=𝑐𝑜𝑛𝑠𝑡
𝐶= 𝑄 𝑉
With dielectric:
Κ:= 𝐶 𝐶 0 = 𝑉 0 𝑉
K>1: relative dielectric constant

2. What happens with the E-field in the presence of dielectric material
𝑸=𝒄𝒐𝒏𝒔𝒕
Κ= 𝑉 0 𝑉 = 𝐸 0 𝐸
𝐸= 𝐸 0 Κ
We know V<V0
E<E0
specifically d
Recall: 𝐸= 𝜎 𝑛𝑒𝑡 𝜖 0
𝜎 𝑛𝑒𝑡
reduced with dielectric material
The surface charge (density) σ on conducting plates does not change but
induced charge σi of opposite sign
𝐸 0 = 𝜎 𝜖 0
𝐸 = 𝜎− 𝜎 𝑖 𝜖 0
and
𝜎 𝑖 =𝜎(1− 1 𝐾 )
𝐸= 𝜎 𝐾𝜖 0
Definition of the permittivity
𝜖=𝐾 𝜖 0
𝐶=𝜖 𝐴 𝑑 and 𝑢= 1 2 𝜖 𝐸 2

3. Dielectrics +Q Example: K1 K2 d/2 E1 E0 V E2 -Q 𝐸 0 = 𝜎 𝜖 0 = 𝑄 𝜖 0 𝐴
𝐸 0 = 𝜎 𝜖 0 = 𝑄 𝜖 0 𝐴
V= 𝐸 1 𝑑 𝐸 2 𝑑 2
= 𝑄 𝜖 0 𝐴 𝐾 1 + 𝑄 𝜖 0 𝐴 𝐾 2 𝑑 2 = 𝑄𝑑 2 𝜖 0 𝐴 ( 1 𝐾 𝐾 2 )
𝐸 1 = 𝐸 0 𝐾 1 = 𝑄 𝜖 0 𝐴 𝐾 1
𝐸 2 = 𝐸 0 𝐾 2 = 𝑄 𝜖 0 𝐴 𝐾 2
𝐶= 𝑄 𝑉 = 𝑄 𝑄𝑑 2 𝜖 0 𝐴 ( 1 𝐾 𝐾 2 ) = 2 𝜖 0 𝐴 𝐾 1 𝐾 2 𝑑( 𝐾 1 + 𝐾 2 )
𝜎 1 =𝜎(1− 1 𝐾 1 )
𝜎 2 =𝜎(1− 1 𝐾 2 )
𝑈= 1 2 𝑄𝑉= 𝑄 2 𝑑 4 𝜖 0 𝐴 1 𝐾 𝐾 2 𝑎𝑛𝑑 𝑢= 𝑈 𝐴𝑑 = 1 4 𝜖 0 ( 𝑄 𝐴 ) 𝐾 𝐾 2 = 𝜖 ( 𝐸 1 𝐾 1 ) 𝐾 𝐾 2
= 𝜖 ( 𝐸 2 𝐾 2 ) 𝐾 𝐾 2

4. 24.4 Dielectrics High Voltage
Cr2O3
Ground
High Voltage
Air
Dielectric breakdown or Dielectric strength

5. Gauss’s Law in Dielectrics
Recall: 𝑄 𝑒𝑛𝑐𝑙 𝜖 0 = 𝐸 ∙ 𝑑𝐴
𝑄 𝑒𝑛𝑐𝑙 = 𝜎− 𝜎 𝑖 𝐴
Conductor
Dielectrics
𝐸 =0
𝐸 ≠0 𝜎
−𝜎 𝑖
𝐸 ∙ 𝑑𝐴 =𝐸𝐴
𝐸𝐴= 𝜎− 𝜎 𝑖 𝐴 𝜖 0
𝜎 𝑖 =𝜎(1− 1 𝐾 ) A
𝐸𝐴= 𝜎𝐴 𝐾 𝜖 0
𝑄 𝑒𝑛𝑐𝑙−𝑓𝑟𝑒𝑒 𝜖 0 = 𝐾 𝐸 ∙ 𝑑𝐴

6. Gauss’s Law in Dielectrics
Example:
Capacitance of half filled spherical capacitor
𝑄 𝑒𝑛𝑐𝑙−𝑓𝑟𝑒𝑒 𝜖 0 = 𝐾 𝐸 ∙ 𝑑𝐴 K E1
𝑄 𝜖 0 = 𝐾 𝐸 ∙ 𝑑𝐴 =𝐾 𝐸 1 2𝜋 𝑟 2 + 𝐸 2 2𝜋 𝑟 2 ra
𝑄 1 𝜖 0
𝑄 2 𝜖 0 r rb
𝐸 1 = 𝑄 1 2𝜖 0 𝐾𝜋 𝑟 2 E2
𝐸 2 = 𝑄 2 2𝜖 0 𝜋 𝑟 2
𝑉= 𝑟 𝑎 𝑟 𝑏 𝐸 1 𝑑𝑟= 𝑄 1 ( 𝑟 𝑏 − 𝑟 𝑎 ) 2𝜖 0 𝐾𝜋 𝑟 𝑎 𝑟 𝑏 𝑄 1 = 2𝜖 0 𝐾𝜋 𝑟 𝑎 𝑟 𝑏 𝑉 ( 𝑟 𝑏 − 𝑟 𝑎 )
𝑄= 𝑄 1 + 𝑄 2 = 2𝜖 0 𝜋 𝑟 𝑎 𝑟 𝑏 𝑉 𝑟 𝑏 − 𝑟 𝑎 (𝐾+1)
𝑉= 𝑟 𝑎 𝑟 𝑏 𝐸 2 𝑑𝑟= 𝑄 2 ( 𝑟 𝑏 − 𝑟 𝑎 ) 2𝜖 0 𝜋 𝑟 𝑎 𝑟 𝑏 𝑄 2 = 2𝜖 0 𝜋 𝑟 𝑎 𝑟 𝑏 𝑉 ( 𝑟 𝑏 − 𝑟 𝑎 )
𝐶= 𝑄 𝑉 = 2𝜖 0 𝜋 𝑟 𝑎 𝑟 𝑏 (𝐾+1) ( 𝑟 𝑏 − 𝑟 𝑎 )
lim Κ→1 2𝜖 0 𝜋 𝑟 𝑎 𝑟 𝑏 (𝐾+1) ( 𝑟 𝑏 − 𝑟 𝑎 ) = 4𝜖 0 𝜋 𝑟 𝑎 𝑟 𝑏 ( 𝑟 𝑏 − 𝑟 𝑎 ) = C empty
Check: K->1 needs to reproduce empty

7. Molecular Model of induced Charge

8. Clicker question
A conductor is an extreme case of a dielectric, since if an electric field is applied to a conductor, charges are free to move within the conductor to set up “induced charges”. What is the dielectric constant of a perfect conductor?
K = 0
K =
A value depends on the material of the conductor