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Wize University Physics Textbook (Master) > DC Circuits

Dielectrics

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Dielectrics

A dielectric is an insulator that has the ability to be polarized. When placed inside an electric field, a net dipole moment is created, with each atom or molecule contributing its own dipole moment.










This causes a small electric field that opposes the existing electric field, so the net electric field between the plates of a capacitor will be smaller:

 E=E0κ \boxed{ \ E=\frac{E_0}{\kappa} \ }
  • EE is the effective electric field with the dielectric
  • E0E_0 is the electric field without the dielectric
  • κ\kappa is the dielectric constant specific to the material

Wize Concept
For vacuum we have κ=1\kappa=1. For other materials we have κ>1\kappa>1.











This in turn means that the potential difference is reduced:

 V=V0κ \boxed{ \ V=\dfrac{V_0}{\kappa} \ }
  • VV is the effective potential difference with the dielectric
  • V0V_0 is the potential difference without the dielectric


Since the charge on the capacitor is held the same, and capacitance is inversely proportional to voltage, the capacitance increases by a factor of κ\kappa:

 C=κC0 \boxed{\ C=\kappa C_0 \ }
  • CC is the effective capacitance with the dielectric
  • C0C_0 is the capacitance without the dielectric


For a parallel plate capacitor this becomes:
 C=κ ε0Ad \boxed{\ C=\kappa\ \frac{\varepsilon_0A}{d} \ }
  • AA is the area of the plates
  • dd is the distance between the plates
  • ε0\varepsilon_0 is the permittivity of free space, ε0=8.854×10−12\varepsilon_0=8.854\times10^{-12} F/m


Wize Concept
  • The dielectric strength is the maximum electric field intensity that can be produced in the dielectric (it can be around a million volts per meter).
  • If the applied voltage becomes too large, dielectric breakdown will occur.



Exam Tip
  • If you have layers of dielectric materials parallel to the plates, consider each as a capacitor in series.
  • If you have layers of dielectric materials perpendicular to the plates, consider each as a capacitor in parallel.


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Example: Three Dielectrics


Find the capacitance of the planar capacitor shown below. The charge on each plate is QQ . Each of the three dielectrics occupies the same volume.




This is equivalent to having three capacitors in parallel with each other.

The equivalent capacitance is therefore:

Ceq=C1+C2+C3C_{eq}=C_1+C_2+C_3


The capacitance of each is given by C=κ ε0(A/3)dC=\kappa \ \dfrac{\varepsilon_0(A/3)}{d}, so we get:


Ceq=κ1ε0A3d+κ2ε0A3d+κ3ε0A3dC_{eq}=\dfrac{\kappa_1\varepsilon_0A}{3d}+\dfrac{\kappa_2\varepsilon_0A}{3d}+\dfrac{\kappa_3\varepsilon_0A}{3d}

=ε0A3d (κ1+κ2+κ3)=\dfrac{\varepsilon_0A}{3d}\ (\kappa_1+\kappa_2+\kappa_3)


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Practice: Three Dielectrics Again


A capacitor is filled with three dielectric materials with different dielectric constants as shown in the picture. The first and the second materials are spread over half the area AA, and have half the thickness dd of the capacitor. The third material is spread over the entire area, and also has half the thickness of the capacitor.

a) Find an expression for the effective capacitance in terms of the dielectric constants and the capacitance CC without any dielectrics inside.

b) Given κ1=2\kappa_1=2, κ2=3\kappa_2=3 and κ3=4\kappa_3=4 , verify that the effective capacitance is larger than CC.