KAHIBARO
Table of Contents
Insulating Materials Inside Capacitors
A dielectric is an insulating material placed between the conductors of a capacitor. Common dielectrics include air, glass, plastic, paper, ceramic, and mica. Unlike conductors, dielectrics do not allow charges to move freely through the material. Even so, they strongly affect how a capacitor behaves.
When a dielectric is inserted between the plates of a capacitor, the capacitance increases. This means the capacitor can store more charge for the same potential difference, or equivalently, the same charge will produce a smaller potential difference.
A dielectric is an insulator that increases the capacitance of a capacitor.
For a capacitor completely filled with a dielectric,
$$
C = \kappa C_0
$$
where $C_0$ is the capacitance without the dielectric and $\kappa$ is the dielectric constant, also called the relative permittivity.
Here, $\kappa$ is a number greater than 1 for ordinary dielectric materials. Vacuum has $\kappa = 1$, and air is very close to 1.
Why Capacitance Increases
To understand why capacitance increases, imagine a parallel plate capacitor connected to a battery. The battery creates an electric field between the plates. If a dielectric is placed between them, the material responds to the field. Its positive and negative charges shift slightly in opposite directions inside the atoms or molecules. This effect reduces the effective electric field inside the capacitor.
Because the electric field becomes weaker for a given free charge on the plates, the potential difference between the plates decreases. Since capacitance is defined by $C = Q/V$, a smaller $V$ for the same $Q$ means a larger capacitance.
If the capacitor remains connected to a battery, the voltage is fixed. Then the increased capacitance allows more charge to flow onto the plates.
Dielectric Constant
The dielectric constant tells us how strongly a material increases capacitance compared with vacuum.
For a parallel plate capacitor without dielectric,
$$
C_0 = \frac{\varepsilon_0 A}{d}
$$
With a dielectric completely filling the space,
$$
C = \frac{\kappa \varepsilon_0 A}{d}
$$
Here, $A$ is the plate area, $d$ is the plate separation, and $\varepsilon_0$ is the permittivity of free space.
It is often convenient to define the permittivity of the material as
$$
\varepsilon = \kappa \varepsilon_0
$$
Then the capacitance becomes
$$
C = \frac{\varepsilon A}{d}
$$
For a parallel plate capacitor fully filled with a dielectric,
$$
C = \frac{\kappa \varepsilon_0 A}{d}
$$
Larger $\kappa$ means larger capacitance.
Microscopic Picture
Inside a dielectric, charges cannot travel across the material as they do in a conductor. Instead, the electric field slightly distorts the charge distribution within atoms or molecules. In some materials, molecules that already have separated positive and negative regions tend to rotate and align with the field. In others, the electron clouds shift relative to the nuclei.
This creates induced charges on the surfaces of the dielectric. These induced charges produce an electric field opposite to the original field between the capacitor plates. The total field becomes smaller than it would be in vacuum.
A full treatment of this charge separation belongs to the topic of polarization, but the main idea here is simple. The dielectric weakens the internal electric field and therefore increases capacitance.
Effect on Electric Field and Voltage
For a capacitor carrying a fixed free charge $Q$, the dielectric changes the electric field and voltage as follows:
$$
E = \frac{E_0}{\kappa}
$$
and
$$
V = \frac{V_0}{\kappa}
$$
where $E_0$ and $V_0$ are the field and voltage without the dielectric.
This is true when the dielectric completely fills the region between the plates.
If the capacitor is isolated, meaning not connected to a battery, the charge stays constant and the voltage drops.
If the capacitor is connected to a battery, the voltage stays constant and the charge increases to
$$
Q = CV = \kappa C_0 V
$$
So the effect depends on whether charge or voltage is held fixed.
With a dielectric fully inserted:
For fixed charge,
$$
E = \frac{E_0}{\kappa}, \qquad V = \frac{V_0}{\kappa}
$$
For fixed voltage,
$$
Q = \kappa Q_0
$$
Two Common Situations
The behavior of a capacitor with a dielectric is easiest to understand by comparing two cases.
| Situation | Quantity unchanged | What changes |
|---|---|---|
| Isolated capacitor | $Q$ | $V$ decreases, $E$ decreases, $C$ increases |
| Capacitor connected to battery | $V$ | $Q$ increases, $C$ increases |
This distinction is very important in capacitor problems.
Energy and Dielectrics
A dielectric also affects the energy stored in a capacitor. The result depends again on whether charge or voltage is fixed.
If charge is fixed,
$$
U = \frac{Q^2}{2C}
$$
Since $C$ increases when the dielectric is inserted, the energy decreases.
If voltage is fixed,
$$
U = \frac{1}{2}CV^2
$$
Since $C$ increases and $V$ stays constant, the energy increases.
So inserting a dielectric can either decrease or increase stored energy, depending on the physical situation.
Dielectric Strength
Real dielectric materials have a limit to how strong an electric field they can withstand. If the field becomes too large, the material breaks down and begins to conduct. This is called dielectric breakdown.
The maximum safe electric field is called the dielectric strength. If the field in a capacitor exceeds this value, sparks or permanent damage may occur.
This property is important in practical capacitor design, because a good dielectric should not only raise capacitance but also tolerate high electric fields.
A dielectric increases capacitance, but every dielectric has a maximum electric field it can withstand.
If the electric field exceeds the dielectric strength, breakdown occurs.
Typical Dielectric Materials
Different materials have different dielectric constants and dielectric strengths.
| Material | Approximate $\kappa$ |
|---|---|
| Vacuum | 1.0 |
| Air | 1.0006 |
| Paper | 2 to 4 |
| Glass | 4 to 10 |
| Mica | 5 to 7 |
| Ceramic | varies widely |
| Water | about 80 |
A large dielectric constant is often useful, but other factors matter too, such as stability, cost, temperature behavior, and breakdown strength.
Visualizing a Dielectric in a Parallel Plate Capacitor
In this sketch, the dielectric fills the region between the plates. The electric field points from the positive plate to the negative plate, but its magnitude is reduced compared with the vacuum case.
Summary Relationship
The main role of a dielectric is to make a capacitor more effective at storing charge.
Key results for a dielectric completely filling a capacitor:
$$
C = \kappa C_0
$$
$$
C = \frac{\kappa \varepsilon_0 A}{d}
$$
For fixed charge,
$$
V = \frac{V_0}{\kappa}, \qquad E = \frac{E_0}{\kappa}
$$
For fixed voltage,
$$
Q = \kappa Q_0
$$
Dielectrics are essential in real capacitors because they increase capacitance, help separate the plates electrically, and allow practical devices to store useful amounts of energy in small spaces.