Fields

• 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
• Similarities between gravitational and electric fields

  • Both follow an inverse-square law
  • Both use field lines to be represented
  • Both have equipotential surfaces
• Differences between gravitational and electric fields

  • In gravitational fields, the force exerted is always attractive, while in electric fields the force can be either repulsive or attractive
  • Electric force acts on charge, while gravitational force acts on mass
• 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, as shown by the parallel and equally spaced field lines
• Radial gravitational field


  The force exerted depends on the position of the object in the field, as an object moves further away from the centre, the magnitude of the force would decrease because the distance between the field lines increases
• 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
• Gravitational potential (V)


  Is inversely proportional to the distance between the centres of the two objects (r)
• Gravitational field strength (g)

  Can be measured by drawing a tangent to the gravitational potential (V) vs distance (r) curve and calculating its gradient, then multiplying by -1
• Gravitational field strength (g)

  The area under the gravitational field strength (g) vs distance (r) curve 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 its 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, where the object's kinetic energy is equal to the magnitude of its gravitational potential energy
• Synchronous orbit


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


  Follows a specific geosynchronous orbit, meaning their orbital period is 24 hours and they always stay above the same point on the Earth, orbiting directly above the equator
• Low-orbit satellites


  Have significantly lower orbits than geostationary satellites, therefore they travel much faster meaning their orbital periods are much smaller
• 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 the Coulomb's law formula, and for a charged sphere, charge may be assumed to act at the centre of the sphere
• The magnitude of electrostatic forces between subatomic particles is magnitudes greater than the magnitude of gravitational forces, this is because the masses of subatomic particles are incredibly small whereas their charges are much larger
• 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

  3. F = 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. F = 2.30 x 10^-5 N
• Ratio of electric force over gravitational force

  F_electric/F_gravitational = (2.30 x 10^-5 N) / (4.65 x 10^-41 N) = 4.94 x 10^35
• The electrostatic force between the two protons is 4.94 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

  3. d = ΔV/E

  4. Work done = ΔV x Q
• 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>