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 ↓


Electric field and electric potential


In the field of electromagnetism, particularly within the branch of electrostatics, we often deal with two fundamental concepts: electric field and electric potential. These concepts are crucial for explaining how electric charges interact in space, affecting everything from the simplest circuits to the most complex electronic devices.

What is electric field?

The electric field is the region around a charged particle where a force will be experienced by other charges. Imagine you have a small charged object called a "test charge." If you place this test charge near another charged object, it will feel a force. The space where this interaction occurs is called an electric field.

The strength and direction of the electric field are described by the electric field vector, usually denoted by E The electric field generated by a point charge Q can be calculated using the formula:

E = k * |Q| / r²

Where:

  • E is the magnitude of the electric field
  • k is the Coulomb constant (8.99 x 10^9 N m²/C²)
  • Q is the charge that produces the field
  • r is the distance from the charge to the point of interest

The direction of the electric field is always directed away from the positive charge and towards the negative charge. Here is a simple visual representation:

Why

Above, the red dot represents the positive charge Q, and the lines show the direction of the electric field radiating outward.

Example of electric field calculation

Suppose you have a charge of 5 µC located 2 m from the point in space where the test charge is placed. To find the electric field at that point, use the formula:

E = k * 5 x 10^-6 C / (2 m)²
E = 8.99 x 10^9 N m²/C² * 5 x 10^-6 C / 4 m²
E = 11237.5 N/C

The electric field is thus directed 11,237.5 N/C away from the charge.

What is electric potential?

Electric potential is a measure of the work done by an electric field in moving a unit positive charge from one point to another. It is a scalar quantity, in contrast to the electric field, and is represented by V We often refer to the potential difference between two points as "voltage."

The electric potential V due to a point charge Q is given by:

V = k * Q / r

Where:

  • V is the electric potential
  • k is the Coulomb constant
  • Q is the charge
  • r is the distance from the charge to the point

Relation between electric field and electric potential

The relationship between electric field and electric potential is one of the main concepts in electrostatics. Electric field is the gradient or spatial rate of change of electric potential.

In simple terms, the electric field is the "slope" of the potential landscape. Mathematically, it is expressed as:

E = -dV/dr

This negative sign indicates the direction of maximum decrease in potential. The electric field points from high potential regions to low potential regions.

Example of electric potential calculation

Consider a charge of 5 µC located 2 m away from the point where we want to calculate the potential. The potential at this point is:

V = k * 5 x 10^-6 C / 2 m
V = 8.99 x 10^9 N m²/C² * 5 x 10^-6 C / 2 m
V = 22487.5 V

The electric potential at this point is 22487.5 volts.

Applications and further analysis

Understanding electric fields and potentials is fundamental to many applications, including designing electrical circuits, capacitors, and even fields such as medical imaging and electronic device engineering.

Electric field lines

Electric field lines provide a visual representation of the strength and direction of the field. These lines emanate from positive charges and end at negative charges. The density of the lines indicates the field strength - closer lines mean the field is stronger.

,,

In the visualization above, the red and blue circles are positive and negative charges, respectively. The lines represent electric field lines going from the positive to the negative charge.

Potential energy in an electric field

In an electric field, a charged particle has potential energy due to its position. This energy changes as the charge moves within the field. For two point charges, the potential energy U is given by:

U = k * Q1 * Q2 / r

Where Q1 and Q2 are their charges respectively and r is the distance between them.

Example problem

Calculate the potential energy between two point charges: 3 µC and 4 µC separated by a distance of 0.5 m:

U = k * 3 x 10^-6 C * 4 x 10^-6 C / 0.5 m
U = 8.99 x 10^9 N m²/C² * 12 x 10^-12 C² / 0.5 m
U = 215.76 x 10^-3 J

The potential energy is 0.21576 joules.

Conclusion

Understanding the electric field and electric potential is important for explaining and predicting the behavior of electrified systems. While the electric field provides insight into the force interactions between charges, the electric potential gives us a scalar measure of the energy landscape within the field.

Both concepts are interconnected, where the electric field is derived from the gradient of the potential, which shows that changes in potential give rise to electric forces that are capable of acting on charges. Mastering these ideas is essential for any aspiring physicist or engineer and is the backbone of electromagnetic theory.


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Electric field and electric potential

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