Gravitation and Fields: A Cheat Sheet

This cheat sheet summarizes key concepts in gravitation, electric fields, and magnetic fields, including Kepler's Laws, Newton's Law of Universal Gravitation, and the behavior of charged particles in fields. It covers fundamental principles, formulas, and applications.

Core Principles

• Kepler's Laws describe planetary motion: elliptical orbits, equal areas in equal times, and a relationship between orbital radius and period.
• Newton's Law of Universal Gravitation states that the force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Electric fields are regions where a charged particle experiences a force. They can be produced by point charges or charged plates.
• Magnetic fields are generated by moving charges or magnetic materials. They exert forces on moving charges and current-carrying wires.
• The inverse square law describes how certain physical properties decrease with the square of the distance from a source.
• Field models (gravitational, electric, magnetic) provide a framework for understanding forces acting at a distance.

Formulas

• $F_g = G\frac{m_1 m_2}{r^2}$
• $F = k\frac{q_1 q_2}{r^2}$
• $E = \frac{kQ}{r^2}$
• $F = qE$
• $F = qvB$
• $F = nIlB$
• $a = \frac{v^2}{r} = \frac{4\pi^2 r}{T^2} = \frac{GM}{r^2}$
• $v = \frac{2\pi r}{T}$
• $r = \frac{mv}{qB}$