Understanding Fields: Gravitational, Electric, and Magnetic

This cheat sheet summarizes the fundamental concepts of gravitational, electric, and magnetic fields, their properties, and the laws governing their interactions, including Kepler's and Newton's laws.

Core Principles

• Gravitational fields are always attractive and are characterized by monopoles (mass).
• Electric fields can be attractive or repulsive and exhibit both monopoles (charge) and dipoles.
• Magnetic fields exist as dipoles (north and south poles) and do not have monopoles.
• Kepler's laws describe planetary motion, stating that orbits are elliptical, areas swept are constant, and the square of the period is proportional to the cube of the radius.
• Newton's law of universal gravitation describes the force between two masses, proportional to the product of their masses and inversely proportional to the square of the distance.
• The inverse square law states that physical properties decrease with the square of the distance from the source.

Formulas

• $F_g = G\frac{m_1 m_2}{r^2}$
• $g = G\frac{M}{r^2}$
• $F = k\frac{q_1 q_2}{r^2}$
• $E = k\frac{Q}{r^2}$
• $F = qE$
• $F = qvB$
• $F = nIlB$
• $a = \frac{v^2}{r} = \frac{4\pi^2 r}{T^2} = \frac{GM}{r^2}$
• $v = \frac{2\pi r}{T}$
• $Q = I \times t$
• $E_k = \frac{1}{2}mv^2$
• $\tau = r_{\perp}F$