Fields and their consequences

• Force field


  An area in which an object experiences a non-contact force
• Force fields


  • Can be represented as vectors, which describe the direction of the force that would be exerted on the object
  • Can be represented as diagrams containing field lines, the distance between field lines represents the strength of the force exerted by the field in that region
• Force fields


  Formed during the interaction of masses, static charge or moving charges
• Types of force fields

  • Gravitational fields
  • Electric fields
• Gravity


  Acts on any objects which have mass and is always attractive
• Newton's law of gravitation


  The magnitude of the gravitational force between two masses is directly proportional to the product of the masses, and is inversely proportional to the square of the distance between them
• Uniform gravitational field


  Exerts the same gravitational force on a mass everywhere in the field
• Radial gravitational field


  The force exerted depends on the position of the object in the field
• Gravitational field strength (g)

  The force per unit mass exerted by a gravitational field on an object
• Gravitational potential (V)


  The work done per unit mass when moving an object from infinity to that point
• Gravitational potential difference (ΔV)


  The energy needed to move a unit mass between two points
• Equipotential surfaces


  Surfaces which are created through joining points of equal potential together, therefore the potential on an equipotential surface is constant everywhere
• No work is done when moving along an equipotential surface
• Gravitational potential (V)


  Inversely proportional to the distance between the centres of the two objects (r)
• The area under the gravitational field strength (g) vs distance (r) graph gives the gravitational potential difference
• Kepler's third law


  The square of the orbital period (T) is directly proportional to the cube of the radius (r)
• Total energy of an orbiting satellite

  Constant, made up of kinetic and potential energy
• Escape velocity


  The minimum velocity an object must travel at to escape the gravitational field at the surface of a mass
• Synchronous orbit


  Where the orbital period of the satellite is equal to the rotational period of the object it is orbiting
• Geostationary satellite


  Orbits directly above the equator with an orbital period of 24 hours, always staying above the same point on Earth
• Low-orbit satellites


  Have significantly lower orbits than geostationary satellites, travel much faster, and have smaller orbital periods
• Coulomb's law


  The magnitude of 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 the charges
• Air can be treated as a vacuum when using Coulomb's law, and for a charged sphere, charge may be assumed to act at the centre of the sphere
• If charges have the same sign the force will be repulsive, and if the charges have different signs the force will be attractive
• The magnitude of electrostatic forces between subatomic particles is magnitudes greater than the magnitude of gravitational forces
• Electric field strength (E)


  The force per unit charge experienced by an object in an electric field
• The gravitational and electrostatic force between two protons with centres 2 pm (2 x 10^-12 m) apart are much larger
• Calculating gravitational force


  1. F = GMm/r^2

  2. F = (6.67 x 10^-11 N m^2/kg^2) x (1.67 x 10^-27 kg) x (1.67 x 10^-27 kg) / (2 x 10^-12 m)^2 = 4.65 x 10^-41 N
• Calculating electrostatic force


  1. F = (1/4πε0) x (Q1 x Q2)/r^2

  2. F = (1/4π x 8.85 x 10^-12 F/m) x (1.6 x 10^-19 C) x (1.6 x 10^-19 C) / (2 x 10^-12 m)^2 = 3.75 x 10^-5 N
• Ratio of electric force over gravitational force


  F_electric/F_gravitational = (3.75 x 10^-5 N) / (4.65 x 10^-41 N) = 8.05 x 10^35
• The electrostatic force between the two protons is 8.05 x 10^35 times greater than the gravitational force
• Calculating electric field strength in a uniform field

  1. E = F/Q

  2. E = V/d
• Calculating electric field strength in a radial field

  E = (1/4πε0) x Q/r^2
• Electric field lines


  • Show the direction of the force acting on a positive charge
  • Uniform field has parallel and equally spaced field lines
  • Radial field has field lines that depend on the distance between the charges
• Calculating work done by moving a charged particle between parallel plates

  1. Work done = F x d

  2. F = E x Q

  3. d = ΔV/E

  4. Work done = Q x ΔV
• Charged particles in a uniform electric field follow a parabolic path, with positive charges moving in the direction of the field and negative charges moving opposite to the field
• Absolute electric potential (V)

  The potential energy per unit charge of a positive point charge at that point in the field
• Calculating electric potential in a radial field

  V = (1/4πε0) x Q/r
• Electric potential difference (ΔV)

  The energy needed to move a unit charge between two points
• Work done in moving a charge across a potential difference is equal to the product of potential difference and charge</b>