Difference Between Permittivity and Permeability with Table & Relation to Speed of Light
Permittivity and permeability are two core concepts in physics that describe how materials respond to electric and magnetic fields. Both play crucial roles in understanding electromagnetic wave propagation, the design of electronic devices, and the foundational laws of electromagnetism.
Permittivity (often represented by Ξ΅) quantifies a material's resistance to forming an electric field, while permeability (denoted by ΞΌ) measures a materialβs ability to permit magnetic field lines. Recognizing the definitions, formulas, units, differences, and applications of these properties is important for mastering electromagnetism and its practical uses.
What is Permittivity?
Permittivity expresses how much a medium resists the formation of an electric field within it. It is especially important when analyzing insulators and dielectrics.
Mathematically, permittivity (Ξ΅) is defined as the ratio of electric displacement (D) to the intensity of the electric field (E) applied:
The SI unit of permittivity is farads per meter (F/m). Materials with high permittivity allow more polarization, requiring more electric flux to generate an opposing electric field. Hence, for high-permittivity dielectrics, the net field strength inside is lower.
The lowest possible permittivity is in a vacuum, denoted as Ξ΅β:
It is often convenient to express a materialβs permittivity as a multiple of vacuum permittivity. This leads to two forms:
- Absolute permittivity (Ξ΅): actual value in a medium
- Relative permittivity (Ξ΅r): ratio of a materialβs permittivity to vacuum permittivity
Ξ΅ = Ξ΅r Γ Ξ΅β
Relative permittivity (dielectric constant) is dimensionless and always greater than one.
What is Permeability?
Permeability measures how easily a material can become magnetized or support the formation of a magnetic field. It is essential for understanding magnetic properties of matter.
Permeability (ΞΌ) is given by the ratio of magnetic field density (B) to the magnetic field strength (H):
Its SI unit is henry per meter (H/m). Permeability also describes the magnetic flux created within a medium when it is placed in an external magnetic field.
The minimum permeability value is that of free space (vacuum), ΞΌβ:
Materials are also compared using:
- Absolute permeability (ΞΌ): refers to the specific value in a material
- Relative permeability: the ratio of absolute permeability to vacuum permeability
The dimensional formula of permeability is [M L T-2 A-2].
Difference Between Permittivity and Permeability
| Property | Permittivity (Ξ΅) | Permeability (ΞΌ) |
|---|---|---|
| Definition | Opposition caused by material during electric field formation | Ability of a material to allow magnetic lines to pass through |
| SI Unit | Farad per meter (F/m) | Henry per meter (H/m) |
| Determined by | Polarization | Magnetization |
| Vacuum/Free Space Value | 8.85 Γ 10-12 F/m | 1.26 Γ 10-6 H/m |
| Creates | Electric field | Magnetic field |
| Typical Device | Capacitor (high permittivity) | Inductor/Transformer core (high permeability) |
Relation Between Permittivity and Permeability
Permittivity and permeability are fundamentally connected through the speed of light (c) in vacuum. According to Maxwellβs equations:
This means that the speed at which electromagnetic waves travel in a vacuum depends on both permittivity and permeability values. Changes in these constants directly affect the speed of light through different materials.
Example Explaining Permittivity
Consider two parallel plates separated by a distance βdβ and filled with air. Molecules between the plates can generate electric dipole moments.
When an external electric field is applied, molecules partially align with the field, creating their own opposing electric field. This reduces the net electric field inside. The phenomenon is known as polarizability.
Higher permittivity means better alignment and greater resistance to the applied field. Materials with low permittivity polarize poorly, offering little resistance.
Example Explaining Permeability
When a magnet is placed near a piece of iron, the iron is attracted because it becomes magnetized and allows magnetic field lines to pass through. The region near the magnet contains magnetic field lines, usually visualized as elliptical loops.
Bringing a non-magnetic material like wood results in no effect. This is due to the low permeability of woodβit cannot support or transmit the magnetic field.
Hence, permeability describes the property of becoming magnetized and supporting a magnetic field when exposed to an external magnetic force.
Key Formulas and Applications
| Quantity | Formula / Value | SI Unit |
|---|---|---|
| Permittivity (Ξ΅) | Ξ΅ = D / E | Farad per meter (F/m) |
| Relative Permittivity (Ξ΅r) | Ξ΅r = Ξ΅ / Ξ΅β | Dimensionless |
| Permeability (ΞΌ) | ΞΌ = B / H | Henry per meter (H/m) |
| Vacuum Permittivity (Ξ΅β) | 8.854 Γ 10-12 | F/m |
| Vacuum Permeability (ΞΌβ) | 4Ο Γ 10-7 β 1.257 Γ 10-6 | H/m |
| Relation to Speed of Light (c) | Ξ΅ Γ ΞΌ = 1 / c2 | β |
Step-by-step Approach to Solving Problems
- Identify whether the problem relates to electric or magnetic fields.
- Write the relevant formula: Ξ΅ = D/E for permittivity, ΞΌ = B/H for permeability.
- Insert values from the problem statement, using standard constants where needed (Ξ΅β or ΞΌβ).
- Ensure SI units are consistent across calculations.
- Calculate and interpret the result in the physics context (e.g., more polarization with high Ξ΅, stronger field lines with high ΞΌ).
Practice and Next Steps
- Review more materials on Permittivity and Permeability for deeper insights and topic-wise notes.
- Apply formulas to solve capacitor and inductor problems, focusing on how dielectric and magnetic materials affect device performance.
- Test your understanding using additional concept checks and practice questions provided by Vedantu.
FAQs on Permittivity and Permeability in Physics: Definitions, Formulas & Examples
1. What is the difference between permittivity and permeability?
Permittivity measures how much a material resists the formation of an electric field, while permeability measures how much a material supports the formation of a magnetic field.
Key points:
• Permittivity (π): Related to electric fields and measured in Farad per meter (F/m).
• Permeability (ΞΌ): Related to magnetic fields and measured in Henry per meter (H/m).
• Permittivity mainly impacts capacitors and electric field strength.
• Permeability mainly impacts inductors, transformer cores, and magnetic field strength.
2. What are the values and units of permittivity and permeability of free space?
The permittivity of free space (πβ) is 8.854 × 10-12 F/m (Farad per meter). The permeability of free space (ΞΌβ) is 4Ο × 10-7 H/m (Henry per meter), approximately 1.257 × 10-6 H/m. These are fundamental constants in electromagnetism.
3. What is the relation between permittivity, permeability, and the speed of light?
The product of permittivity and permeability of free space is related to the speed of light (c) by:
c = 1 / √(ΞΌβπβ)
This means the speed of light in vacuum depends on both electric and magnetic properties of free space.
4. What is the formula for permittivity?
Permittivity (π) is defined as:
π = D / E
Here,
• D = Electric displacement (C/m2)
• E = Electric field intensity (V/m)
Absolute permittivity of a medium is often referenced to the permittivity of free space (πβ).
5. What is the formula for permeability?
Permeability (μ) is defined as:
μ = B / H
Where,
• B = Magnetic flux density (Tesla, T)
• H = Magnetic field strength (A/m)
The absolute permeability of free space is denoted by μ0.
6. What are the symbols and dimensional formulas for permittivity and permeability?
• Permittivity symbol: π (epsilon)
• Permeability symbol: ΞΌ (mu)
• Dimensional formula for permittivity (π): [M-1L-3T4A2]
• Dimensional formula for permeability (ΞΌ): [MLT-2A-2]
7. What is relative permittivity and how is it different from absolute permittivity?
Relative permittivity (πr) is the ratio of the absolute permittivity of a material (π) to the permittivity of free space (πβ).
Formula: πr = π / πβ
• It is a unitless quantity.
• Absolute permittivity has units (F/m); relative permittivity does not.
8. Why are permittivity and permeability important in Physics?
Permittivity and permeability are crucial because:
• They determine how electromagnetic waves propagate through different media.
• They affect the speed of light, capacitance, inductance, and behavior of electric and magnetic fields.
• All electromagnetic phenomena, including electricity, magnetism, and optics, depend on these two fundamental properties.
9. How do you use permittivity and permeability constants in numerical problems?
To solve physics numericals on electric or magnetic fields:
• Identify if the problem involves electric (use πβ) or magnetic (use ΞΌβ) constants.
• Substitute πβ = 8.854 × 10-12 F/m or ΞΌβ = 4Ο × 10-7 H/m as required.
• Apply the correct formula, check units, and solve step by step.
10. What is the difference between absolute and relative permeability?
Absolute permeability (ΞΌ) is the permeability of a material in Henry per meter (H/m).
Relative permeability (ΞΌr) is the ratio between the permeability of a material and that of free space (ΞΌ / ΞΌβ), and is unitless.
11. Why does the speed of light depend on permittivity and permeability?
The speed of light in vacuum (c) is determined by how electric and magnetic fields interact in free space.
According to Maxwell's equations: c = 1 / √(ΞΌβπβ). The lower the permittivity and permeability, the higher the speed of light.
12. Which devices rely on high permittivity or high permeability materials?
• High permittivity materials are used in capacitors for energy storage.
• High permeability materials are used in inductor and transformer cores to enhance magnetic field strength and efficiency.
