Section 7 - Fields and their Consequences

• a force field is a region in which a body experiences a non contact force
• gravitational fields are regions where a mass experiences an attractive force due to gravity
• the force experienced by a mass in a gravitational field is determined by newton's law of gravitation: $F\ =$$\ \frac{Gm_1m_2}{r^2}$
• you can represent gravitational fields with field lines. they:

  • always point towards the centre of mass producing the field
  • show the direction in which a mass would experience a force if places at a point in that field
  • are closer together where the field is stronger
  • are further apart where the field is weaker
  • never cross over eachother
• gravitational field strength is defined as the attractive gravitational force that a unit mass would experience in a given point in the field
• gravitational potential is the amount of work done in moving a unit mass from infinity to a given point in a gravitational field
• gravitational potential is defined as being zero at infinity. work is done to move an object closer into the field, and so gravitational potential is always a negative value
• equipotentials are planes containing points with equal gravitational potential. this means that the amount of work done when an object is moved around these planes is zero
• the orbits of planes and satellites are a result of the gravitational force produced by the body they are orbiting. this force acts as a centripetal force, which results in circular motion
• synchronous orbits have a time period of one day, and so return to the same place in the sky each day
• low orbits orbit at heights of between 160km and 2000km
• geostationary orbits have a time period of one day and stay over the same point above the earth. they must be directly above the equator and travel in the same direction as the earth's rotation
• all charged particles and surfaces produce an electric field around themselves. an electric field is a region where a charged particle experiences a non contact force. unlike gravitational fields, this force can be attractive or repulsive
• electric field lines point in the direction that a positive charge would experience a force and so point from positive to negative
• the force that acts between two charges is determined by coulomb's law.

  if the force has a positive value, it is a/an repulsive force

  if the force has a negative value, it has a/an attractive force
• electric field strength is defined as the electrostatic force that a unit positive charge would experience, at a given point in the field
• the electric field strength around a charge decreases as you move further away from it. the weaker the electric field strength, the less dense the electric field lines are
• electric potential is the amount of work done moving a unit positive charge from infinity to a point in the field
• electric potential difference is the work done moving a positive charge from one point to another. this means that when you move a charge through a potential difference, work is done.
• the capacitance of a capacitor is the amount of charge it can store per unit of potential difference, measured in Farads
• capacitors consist of two metal plates separated by a dielectric. the capacitance of a given capacitor depends on the surface area of the plates, their separation and the dielectric being used
• a polar dielectric consists of lots of polarised molecules each with a positive end and a negative end. when placed in a capacitor, the molecules align and all the positive ends are attracted to the negative plate, and all the negative ends are attracted to the positive plate.
• polar dielectrics in capacitors result in the capacitance increasing since:

  • the polarised molecules each have an electric field around them
  • this electric field opposes the electric field of the capacitor plates
  • consequently the potential difference required to charge the plates decreased

  so if the potential difference is decreases, the capacitance is increased
• E = 1/2 x Q x V

  so the energy stored can also be calculated by determining the area under a charge voltage graph
• the time constant of a capacitor is the time taken to:

  • to charge the capacitor to 1-1/e of its final value
  • to discharge the capacitor to 1/e of its initial value

  (this can be found from the formula)

  
  

  it is the product of the resistance in the circuit and the capacitance of the capacitor
• when a current passes through a wire, a magnetic field is induced around it. this field consists of concentric circles around the wire. the strength depends on:

  • the distance from the wire
  • the strength of the current passing through the wire
• if a current carrying wire is placed in a magnetic field, the two fields interact and a force acts on the wire. the magnitude of this force depends on:

  • the length of the wire
  • the current passing through the wire
  • the magnetic flux density of the field
• magnetic flux density is a measure of the strength of the field. its unit is the Tesla
• when a current carrying wire experiences a force in the field, it is referred to as the motor effect. the magnitude of the force can be calculated using:

  F=BIL

  the direction can be determined using fleming's left hand rule
• fleming's left hand rule:

  • thumb = force
  • pointer finger = field
  • middle finger = current (ie direction of positive charge)
• when a charge moves in a magnetic field, it will experience a force. the magnitude of this force depends on:

  • the magnitude of the charge
  • the magnetic flux density of the field
  • the velocity of the charge

  the equation used to calculate this force is:

  F=BQv
• magnetic flux is a measure of the magnetic field that passes through a given area

  magnetic flux = magnetic flux density x area
• $\phi$ is the symbol for magnetic flux

  B is the symbol for magnetic flux density
• magnetic flux linkage is useful when using coils. this is the magnetic flux multiplied by the number of turns of the coil the field passes through
• if a current carrying conductor moves relative to a magnetic field, an EMF is induced. this is as a result of the charge carriers in the conductor experiencing a force. if the conductor forms a complete loop, a current flows as a result of the induced EMF.
• the law that governs the magnitude of the induced EMF is Faraday's law, which states that:

  • the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linkage
• the law that governs the direction of an induced emf is Lenz's law, which states that:

  • the direction of an induced current is such that it opposes the change that it created it
• an ac generator consists of a metal coil in a magnetic field. as the coil turns, the changing magnetic flux linkage passing through it induces an emf
• in ac generators, the flux linkage varies sinusoidally between +BAN and -BAN
• an oscilloscope is used to show voltage against time.

  • $V_0$ is the peak voltage
  • the average voltage is not the peak voltage, it is the root mean square