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 → Magnetism and Electromagnetism ↓


Magnetic force on moving charges


In physics, magnetism and electromagnetic forces play an important role in understanding how objects and particles behave in magnetic fields. A magnetic field is a force field created by magnetic objects or moving electric charges, which exerts a force on other magnetic objects or charged particles. When we talk about "magnetic force on moving charges," we are referring to the effect of a magnetic field on moving electric charges within that field. This concept is fundamental in electromagnetic theory and has important applications in many areas such as electric motors, generators, and even the way our universe operates.

Understanding magnetic fields

Before going into the details of the magnetic force on moving charges, it is important to understand what a magnetic field is. A magnetic field is a vector field around magnetic substances and electric currents. It consists of invisible force lines that extend from the north pole to the south pole of a magnet. These lines are called magnetic field lines.

NSMagnetic field lines

The density of these lines indicates the strength of the magnetic field. The closer the lines are, the stronger the magnetic field, and vice versa. A magnetic field exerts a force on charges moving through it, and this force depends on the velocity of the charge, the strength of the field, and the charge itself.

Lorentz force

The force experienced by a charge moving in a magnetic field is described by the Lorentz force. It includes both electric and magnetic forces, but we will focus on the magnetic component. For a charge q moving with velocity v in a magnetic field B, the magnetic force F is given by:

F = q(v × B)

Here are the details of the conditions:

  • F is the magnetic force acting on the charge.
  • q is the magnitude of the charge.
  • v is the velocity of the charge.
  • B is the magnetic field vector.
  • × denotes the cross product, resulting in a vector that is perpendicular to both v and B

The direction of the force follows the right-hand rule: if you point your right index finger in the direction of the velocity v and your middle finger in the direction of the magnetic field B, your thumb will point in the direction of the force experienced by the positive charge.

VBF

If the charge is negative, the direction of the force will be opposite. This is important to determine the trajectory of the particle in a magnetic field.

Example calculation

To reinforce this concept, let us consider some example calculations with the magnetic force equation.

Example 1: Positive charge in a uniform magnetic field

Suppose you have a positive charge of 2 C moving at a velocity of 3 m/s perpendicular to a uniform magnetic field of 5 T What is the force experienced by the charge?

Use of the formula:

F = q(v × B)

We insert the values:

F = 2 C × (3 m/s × 5 T) = 30 N

The force experienced by the charge is 30 N in the direction perpendicular to the velocity and the magnetic field.

Example 2: Negative charge path deflection

Now let's see what happens with a negative charge. Consider a -1 C charge moving at a speed of 4 m/s in a uniform magnetic field of 5 T What is the force on this charge?

Again, use the formula:

F = q(v × B)

Entering the values gives:

F = -1 C × (4 m/s × 5 T) = -20 N

The negative sign indicates that the force is in the opposite direction than that of a positive charge. This reversal in direction affects how the charge moves through the magnetic field.

Applications in circular motion

When a charged particle moves perpendicular to a magnetic field, it undergoes uniform circular motion. This happens because the magnetic force acts as a centripetal force, constantly changing the direction of the particle, resulting in circular motion.

For a charge q moving with velocity v in a magnetic field B, the radius r of the circle can be found using the formula for centripetal force:

F = m(v²/r)

Replacing the magnetic force:

q(v × B) = m(v²/r)

Solution for r:

r = m(v/qB)

Thus, the radius of the particle's trajectory is determined by its mass, velocity, charge, and the magnitude of the magnetic field.

Real-world applications

This principle of magnetic force on moving charges is used in a variety of technologies:

  • Electric motors: use magnetic fields to convert electric current into rotational motion.
  • Cyclotrons and synchrotrons: accelerate charged particles to high speeds using magnetic fields.
  • Mass spectrometers: determine the structure and abundance of different isotopes by measuring the charge-to-mass ratio.

Understanding these principles helps scientists and engineers to effectively design and optimize these applications.

Conclusion

In summary, magnetic force on moving charges is a key concept in physics, based on fundamental electromagnetic principles. Its profound implications in both theoretical and applied physics highlight the importance of mastering this subject. The mathematical formulation through the Lorentz force equation provides a quantitative means to predict the behaviour of charges in magnetic fields. From understanding how particles move, to practical applications in technology, this concept provides insights into both the microscopic and macroscopic worlds.


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Magnetic force on moving charges

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