Fields + Their consequences

• Force fields are areas where objects experience non-contact forces
• Force fields can be represented as vectors, showing the direction of the force exerted on the object
• Field lines in diagrams represent force strength, with distance between lines indicating force strength
• Different types of force fields are formed during interactions of masses, static charge, or moving charges
• Gravitational fields are always attractive, while electric fields can be either repulsive or attractive
• Both gravitational and electric fields follow an inverse-square law
• Electric force acts on charge, while gravitational force acts on mass
• Newton's law of gravitation states that the gravitational force between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between them
• Gravitational potential is the work done per unit mass when moving an object from infinity to a point
• Gravitational potential is always negative and decreases as an object moves closer to a mass
• Gravitational potential difference is the energy needed to move a unit mass between two points
• Gravitational field strength can be uniform or radial, with uniform fields exerting the same force everywhere and radial fields having force depend on position
• Gravitational field strength is constant in a uniform field but varies in a radial field
• Escape velocity is the minimum velocity needed to escape a gravitational field
• Synchronous orbits have orbital periods equal to the rotational period of the object being orbited
• Coulomb's law states that the force between two point charges in a vacuum is directly proportional to the product of their charges and inversely proportional to the square of the distance between them
• Electric field strength is the force per unit charge experienced by an object in an electric field
• Electric fields can be uniform or radial, with uniform fields exerting the same force everywhere and radial fields having force depend on distance
• Electric potential at a certain position in any electric field is defined as the work done per unit positive charge on a positive test charged when moved from infinity to that position
• Electric potential is the potential energy per unit charge of a positive point charge at that point in the field
• The absolute magnitude of electric potential is greatest at the surface of a charge
• As the distance from the charge increases, the potential decreases
• Electric potential at infinity is zero
• Formula to find the value of potential in a radial field: V = 1 / (4πE0) * (Q / r)
• ε₀ is the permittivity of free space, Q is the charge, r is the distance from the charge
• The sign of the potential (negative or positive) depends on the sign of the charge (Q)
• When the charge is positive, potential is positive and the charge is repulsive
• When the charge is negative, potential is negative and the force is attractive
• Gradient of a tangent to a potential (V) against distance (r) graph gives the value of electric field strength (E) at that point: E = ΔV / Δr
• Electric potential difference (VΔ) is the energy needed to move a unit charge between two points
• Work done (WΔ) in moving a charge across a potential difference is equal to the product of potential difference and charge: WΔ = Q * VΔ
• Equipotential surfaces have the same potential everywhere
• No work is done when a charge moves along an equipotential surface
• Equipotential surfaces around a point charge form concentric circles
• Capacitance (C) is the charge stored (Q) by a capacitor per unit potential difference (V): C = Q / V
• Relative permittivity (εr) is the dielectric constant of a dielectric, calculated as the ratio of the permittivity of the dielectric to the permittivity of free space: εr = ε/ ε0
• Energy stored by a capacitor (E) is given by the area under a graph of charge (Q) against potential difference (V): QV = 1/2 CV² = 1/2 Q² / C
• To charge a capacitor, connect it in a circuit with a power supply and resistor
• Graph voltage and current against time to measure values
• To discharge a capacitor, connect it to a closed circuit with just a resistor