Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Electromagnetism → Electrostatics ↓


Capacitance and Dielectric


In the fascinating field of electromagnetism, capacitance is a concept that plays a vital role, especially in the design of circuits and many electronic devices. Combined with the concept of dielectrics, it becomes even more powerful in a variety of applications.

What is capacitance?

Capacitance is a measure of a capacitor's ability to store charge per unit voltage. To better understand capacitance, let's first understand what a capacitor is.

The basics: What is a capacitor?

A capacitor is a device that stores electrical energy in an electric field. It consists of two conductors separated by an insulating material called a dielectric. When a potential difference (voltage) is applied across the conductors, an electric field develops in the dielectric, causing a charge to build up on the plates. This is how energy is stored in a capacitor. 

Formula: C = Q / V

Where:

  • C is the capacitance measured in Farads (F).
  • Q is the charge stored in coulombs (C).
  • V is the voltage across the capacitor in volts (V).

Example calculation

If a capacitor stores a charge of 2 coulombs and a voltage of 4 volts is applied across it, the capacitance is given by: 

C = Q / V = 2C / 4V = 0.5F

This means that the capacitance of the capacitor is 0.5 Farad.

Role of dielectric

Dielectrics are insulating materials placed between the plates of a capacitor. They serve several purposes, such as increasing the capacitance without allowing charge to flow between the plates, since they do not conduct electricity.

Effect of dielectric on capacitance

When a dielectric is added, the capacitance of a capacitor increases. The dielectric constant (also called relative permittivity, k) tells how much a dielectric material can increase the capacitance compared to vacuum. The capacitance C with a dielectric is given by: 

C = K * C₀

Where C₀ is the capacitance without dielectric (in vacuum or air), and k is the dielectric constant.

Dielectric insert: a visual example

Dielectric Plate 1 Plate 2

The image above shows a basic capacitor setup with two plates and a dielectric between them. Note that the dielectric does not make contact with the plates, but rather sits in between, increasing the capacitance.

Example calculation with dielectric

Consider a capacitor whose capacitance is C₀ = 1 μF when there is air between its plates. Suppose we fill the space with a dielectric material having a dielectric constant of 2.5. The new capacitance can be calculated as: 

C = 2.5 * 1 μF = 2.5 μF

This increase in capacitance makes the capacitor more effective at storing charge for the same voltage.

Energy stored in a capacitor

A capacitor not only stores charge; it also stores energy. The energy (U) stored in a capacitor can be calculated using the formula: 

U = 1/2 * C * V²

Let us explain with an example. If a capacitor with a capacity of 1 μF is charged to a voltage of 10V, the energy stored will be: 

U = 1/2 * 1 * 10² = 50 μJ

This energy can be used to perform work, such as powering a small light bulb or allowing for data backup in a system before a power outage occurs.

Types of capacitors

There are different types of capacitors, each with unique properties and uses, including:

  • Ceramic Capacitors: Often used for high frequency applications.
  • Electrolytic Capacitors: Suitable for applications requiring high capacitance values.
  • Film capacitors: Provide stable capacitance over a wide range of temperatures.
  • Tantalum Capacitors: Known for good stability and high capacitance in small sizes.

Ceramic capacitor characteristics

Ceramic Clue

A simple ceramic capacitor is shown in the diagram. They are widely used because of their ability to operate up to very high frequencies, their non-polarity, and their relatively low cost.

Practical applications of capacitance and dielectric

Capacitors are used in almost every electronic device. Here are some applications:

  • Energy storage: Capacitors can store energy for later use, such as in camera flash circuits.
  • Power Conditioning: Capacitors smooth out the output of a power supply by filtering out voltage spikes.
  • Signal processing: In audio systems, capacitors block DC current while allowing AC signals to pass through.

A simple circuit example

Imagine a simple RC (resistor-capacitor) circuit where a capacitor is connected in series with a resistor and a power supply. Such circuits are typically used to create delayed or filtered signals. 

              + ------- R ------- C ------- -
             ,
             ,

When the switch is closed, the current will start charging the capacitor. The time it takes to charge the capacitor can be controlled by the resistance and capacitance values.

Conclusion

Understanding capacitance and dielectrics is vital to understanding aspects of electromagnetism and designing efficient electrical and electronic systems. Capacitance allows a device to store energy, while dielectrics increase the efficiency of a capacitor by increasing its ability to store charge. Armed with this understanding, one can appreciate the important role capacitors play in the modern technological world.


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Capacitance and Dielectric

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