Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Electricity and Magnetism → Electrostatics ↓


Coulomb's law and its applications


Introduction to Coulomb's law

Coulomb's law is a fundamental principle in the field of electrostatics, which describes the force between two charged objects. It helps us understand the interactions caused by electric charges. Before we delve deeper into the specifics of Coulomb's law, let's explore some basic properties of electric charges.

There are two types of charges: positive and negative. Like charges repel each other, while unlike charges attract. This can be easily observed by bringing two charged objects close to each other. Coulomb's law quantifies the force between these charges, making it possible to calculate the exact magnitude and direction of this interaction.

Statement of Coulomb's law

According to Coulomb's law, the electric force (F) between two point charges is proportional to the product of the magnitudes of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The mathematical representation of Coulomb's law is given as:

F = k * (|q1 * q2|) / r²

where k is the Coulomb constant. In appropriate units, this constant is approximately:

k ≈ 8.99 x 109 N m²/C²

Force is a vector, which means it has both magnitude and direction. The direction is such that the force is along the line connecting the two charges, repelling if the charges are like, and attractive if they are opposite.

Visual representation

Q1 F Q2 R

This diagram shows the force F acting between two charges Q1 and Q2 separated by a distance r.

SI units in Coulomb's law

To apply Coulomb's law correctly, it is necessary to use SI units for charge and distance. The charge must be in coulombs (C), the distance must be in meters (m), and the resultant force will be in newtons (N).

For example, if q1 = 1 C, q2 = 2 C, and r = 1 m, then the force F is calculated as:

F = (8.99 x 109 N m²/C²) * ((1 C * 2 C) / (1 m)²) = 1.798 x 1010 N

Examples of Coulomb's law calculation

Let us consider some examples to understand how to use Coulomb's law in practice.

Example 1: Charges in a line

Two charges q1 = 3 μC and q2 = 4 μC are at a distance of 0.5 m from each other. Calculate the force between them.

Convert charges from microcoulombs (μC) to coulombs (C):

q1 = 3 μC = 3 x 10-6 C
q2 = 4 μC = 4 x 10-6 C

Now apply Coulomb's law:

F = (8.99 x 109 N m²/C²) * ((3 x 10-6 C * 4 x 10-6 C) / (0.5 m)²)
F = 0.4315 N

The force between the charges is 0.4315 N, and since both charges are positive, it will be a repulsive force.

Example 2: Opposite charges

Consider a positive charge of q1 = 1 μC and a negative charge of q2 = -1 μC, located at a distance of 1 m from each other. What is the force between these charges?

First, convert to coulombs:

q1 = 1 μC = 1 x 10-6 C
q2 = -1 μC = -1 x 10-6 C

Apply Coulomb's law:

F = (8.99 x 109 N m²/C²) * ((1 x 10-6 C * -1 x 10-6 C) / (1 m)²)
F = -8.99 N

The magnitude of the force is 8.99 N, and since the charges are opposite, it will be attractive.

Applications of Coulomb's law

Coulomb's law is essential in a variety of fields and applications:

Electric field calculation

This law helps in understanding the electric field. The electric field E produced by a point charge q located at a distance r is described as:

E = k * |q| / r²

This equation describes how a point charge affects the space around it.

Forces in molecules

Understanding the forces between atomic and molecular structures is fundamental to chemistry and physics. Electrostatic forces involve the attraction and repulsion within molecules, which affect the structure and stability of substances.

Design of electrical components

Coulomb's law is important for designing capacitors and other electric circuit components, which rely heavily on charge interactions and storage capabilities. Understanding interactions at the charge level helps engineers design better and more efficient circuits.

Visual example

Q1 Q2 F

In this diagram, the electrostatic force F results from the interaction between two charged particles, Q1 and Q2.

Considerations and limitations

Coulomb's law is a powerful tool, but it only works under specific circumstances:

  • Point charge: This law is accurate for point charges, where the size of the charge is negligible compared to the distance between them.
  • Vacuum: The Coulomb constant, k, assumes that the medium between the charges is a vacuum. Different mediums will require adjustments based on the permittivity of the medium.
  • Non-relativistic motion: This law is valid when charges move at non-relativistic speeds, where magnetic fields are not important.

Conclusion

Coulomb's law provides the basic knowledge for understanding electric forces between charges. It helps solve problems related to electric forces, electric field strength and potential. Its applications are wide-spread in physics, chemistry and engineering, providing solutions to problems ranging from microscopic to macroscopic scales. Understanding of this law is important for further study and applications in electromagnetism and circuit design.


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