1. Concept Overview
A dielectric is an insulating material placed between the plates of a capacitor. It does not conduct electricity, but it reacts to electric fields in an important way. When an electric field is applied, the molecules inside the dielectric become slightly rearranged, creating an internal field that influences the total electric field between the plates. This effect is called polarisation.
2. What Is a Dielectric?
Dielectrics are materials that do not allow free movement of charges but can have their internal charge distribution distorted under an electric field. Examples include glass, mica, ceramic, rubber, air and vacuum.
3. Polarisation of Dielectrics
Polarisation is the process by which positive and negative charges within a dielectric shift slightly in opposite directions when an electric field is applied. This creates induced dipoles inside the material.
3.1. Types of Polarisation
- Electronic polarisation: Shift of electron clouds relative to nuclei.
- Ionic polarisation: Positive and negative ions shift relative to each other.
- Orientation polarisation: Permanent dipoles rotate to align with the field.
3.2. Effect of Polarisation
Polarisation creates an internal electric field that opposes the external field. As a result, the effective electric field inside the dielectric becomes smaller.
4. Dielectric Constant
The dielectric constant (also called relative permittivity) is a measure of how much a dielectric reduces the electric field inside it.
4.1. Definition
If the electric field inside the capacitor without dielectric is \( E_0 \) and with dielectric is \( E \), then:
\( \kappa = \dfrac{E_0}{E} \)
4.2. Typical Values
Air ≈ 1, Glass ≈ 5–10, Mica ≈ 4–7, Ceramics can be much higher (hundreds or more).
5. Effect of Dielectric on Capacitance
Placing a dielectric between the plates increases the capacitance because the reduced electric field allows more charge to be stored for the same voltage.
5.1. Formula
Capacitance with dielectric:
\( C = \kappa C_0 = \kappa \dfrac{\varepsilon_0 A}{d} \)
where \( C_0 \) is the capacitance without dielectric.
5.2. Interpretation
Higher dielectric constant → more charge stored → higher capacitance.
6. Dielectric Strength
Every dielectric can withstand only a certain maximum electric field before it breaks down and becomes conducting.
6.1. Definition
Dielectric strength is the maximum electric field a material can tolerate without breakdown.
6.2. Examples
Air: ~3 × 10⁶ V/m, Mica: ~10 × 10⁶ V/m, Oil: varies widely.
7. Microscopic View of a Dielectric in a Capacitor
Inside the dielectric, millions of tiny dipoles form due to polarisation. These dipoles create an internal field that opposes the applied field. This cancellation lowers the effective field, allowing more charge to build on the capacitor plates for the same external voltage.
8. Energy Stored with Dielectric
Because capacitance increases when a dielectric is inserted, the energy stored in the capacitor changes depending on whether charge or voltage is fixed.
8.1. Case 1: Voltage Constant (Connected to Battery)
Energy increases because the capacitor stores more charge:
\( U = \dfrac{1}{2} C V^2 \)
8.2. Case 2: Charge Constant (Isolated Capacitor)
Energy decreases because increased capacitance spreads the same charge across more space:
\( U = \dfrac{Q^2}{2C} \)
9. Worked Examples
9.1. Example 1: Capacitance Increase
A capacitor of \( C_0 = 2\,\mu F \) is filled with a dielectric of \( \kappa = 4 \).
New capacitance: \( C = 4 \times 2 = 8\,\mu F \).
9.2. Example 2: Effect on Energy (Voltage Constant)
If \( V = 100 \text{ V} \), energy stored initially is:
\( U_0 = \dfrac{1}{2} C_0 V^2 = \dfrac{1}{2} \times 2 \times 10^{-6} \times 100^2 = 0.01 \text{ J} \).
With dielectric: \( U = \dfrac{1}{2} C V^2 = \dfrac{1}{2} \times 8 \times 10^{-6} \times 100^2 = 0.04 \text{ J} \).
Energy quadruples.
10. Physical Interpretation
Dielectrics don’t conduct electricity, but their molecules rearrange in an electric field—like tiny springs stretching or rotating. This reaction reduces the net field inside, making it easier to store charge. This is why capacitors always use dielectrics, and why different materials give different capacitor ratings.