Interesting electromagnetic force

 

The electromagnetic force is one of the four fundamental forces of nature (along with gravity, the strong nuclear force, and the weak nuclear force). It governs the interactions between charged particles and is responsible for most everyday phenomena, from electricity and magnetism to light and chemistry.

Key Aspects of the Electromagnetic Force:

1. Coulomb's Law – Describes the force between two stationary charged particles:

   $$F=k_e\frac{q_1{q}_2}{r^2}$$

   • $F$: Force (attractive if opposite charges, repulsive if like charges)

   • $k_e$: Coulomb's constant ()

   • $q_1,q_2$: Electric charges

   • $r$: Distance between charges

2. Lorentz Force – Describes the force on a moving charge in an electromagnetic field:

   $$\mathbf{F}=q(\mathbf{E}+\mathbf{v}\times \mathbf{B})$$

   • $\mathbf{E}$: Electric field

   • $\mathbf{B}$: Magnetic field

   • $\mathbf{v}$: Velocity of the charge

3. Maxwell’s Equations – The foundation of classical electromagnetism:

   • Gauss’s Law (Electric): $\mathrm{\nabla }\cdot \mathbf{E}=\frac{\rho }{{ϵ}_0}$

   • Gauss’s Law (Magnetism): $\mathrm{\nabla }\cdot \mathbf{B}=0$ (No magnetic monopoles)

   • Faraday’s Law: $\mathrm{\nabla }\times \mathbf{E}=-\frac{\mathrm{\partial }\mathbf{B}}{\mathrm{\partial }t}$ (Changing B-field induces E-field)

   • Ampère’s Law (with Maxwell’s correction): $\mathrm{\nabla }\times \mathbf{B}={\mu }_0\mathbf{J}+{\mu }_0{ϵ}_0\frac{\mathrm{\partial }\mathbf{E}}{\mathrm{\partial }t}$

4. Quantum Electrodynamics (QED) – The quantum field theory of electromagnetism, describing how photons mediate the electromagnetic force between charged particles.

Interesting Phenomena Due to Electromagnetic Force:

• Light is an electromagnetic wave – Oscillating electric and magnetic fields propagate at the speed of light ($c=3\times {10}^8\text{m/s}$).

• Superconductivity – At low temperatures, some materials expel magnetic fields (Meissner effect) and conduct electricity with zero resistance.

• Magnetic Levitation (Maglev) – Strong magnetic fields can levitate trains, reducing friction.

• Chemical Bonds – Electromagnetic interactions between electrons and nuclei form molecules.

• Electromagnetic Radiation – From radio waves to gamma rays, all are manifestations of the EM force.

Fun Fact:

The electromagnetic force is about ${10}^{36}$ times stronger than gravity, yet it doesn’t dominate the universe at large scales because positive and negative charges tend to cancel out, whereas gravity is always attractive.