Important Theorems and Laws in Physics for UPSC Physics Optional Subject

1. Newton's Laws of Motion:
- Newton's First Law states that an object at rest will remain at rest, and an object in motion will continue moving with a constant velocity, unless acted upon by an external force.
- Newton's Second Law states that the force acting on an object is directly proportional to its mass and the acceleration produced. It is given by the equation F = ma.
- Newton's Third Law states that for every action, there is an equal and opposite reaction.

2. Law of Gravitation:
- The Law of Gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. It is given by the equation F = G * (m1 * m2) / r^2, where G is the gravitational constant.

3. Laws of Thermodynamics:
- The First Law of Thermodynamics, also known as the Law of Conservation of Energy, states that energy cannot be created or destroyed, only converted from one form to another.
- The Second Law of Thermodynamics states that the entropy of an isolated system will always increase over time.
- The Third Law of Thermodynamics states that as the temperature of a system approaches absolute zero, the entropy of the system approaches a minimum value.

4. Ohm's Law:
- Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to its resistance. It is given by the equation V = IR, where V is voltage, I is current, and R is resistance.

5. Maxwell's Equations:
- Maxwell's Equations describe the behavior of electric and magnetic fields. They consist of four equations that relate electric and magnetic fields to their sources, such as charges and currents.

6. Einstein's Theory of Relativity:
- Einstein's Theory of Relativity consists of two parts: the Special Theory of Relativity and the General Theory of Relativity. The Special Theory of Relativity deals with the behavior of objects moving at speeds close to the speed of light, while the General Theory of Relativity deals with the effects of gravity on spacetime.

7. Schrödinger's Wave Equation:
- Schrödinger's Wave Equation is a fundamental equation in quantum mechanics that describes the wave-like behavior of particles. It allows us to calculate the probability distribution of finding a particle in a particular state.

8. Conservation Laws:
- Conservation of Energy: Energy cannot be created or destroyed, only converted from one form to another.
- Conservation of Momentum: The total momentum of an isolated system remains constant.
- Conservation of Charge: The total electric charge of an isolated system remains constant.

These theorems and laws form the foundation of classical and modern physics. Understanding and applying them correctly is crucial for a thorough understanding of the subject.