7.3 electric fields

• Coulombs law of attraction 

  • Force between two point charges in a vacuum
  • $F=$$Q_1Q_2/4\pi\epsilon_0r^2$
  • Force is directly proportional to the product of their charges
  • Force is inversely proportional to the square of their distances apart
  • $F=$$kQ_1Q_2/r^2$ $k=$$1/4\pi\epsilon_0$
  • $\epsilon_0=$$8.85*$$10^-12$    $C^2N^-1m^-2$  or  $Fm^-1$ - permittivity of free space
  • Air can be treated as a vacuum
  • For a charged sphere, charge is considered to be at the centre
• Electric field - a region around an object of charge, where a charged particle will experience a force

  Electric field line - direction of force on a positive test charge at that point

  Electric field strength - strength of force of a positive charge at that point

  • If a charged object enters an electric field, it will experience an electrostatic force
  • The force an object in an electric field experiences at a particular point is proportional to the object’s charge
  • F∝Q     F=kQ   where k is the constant of attraction

  
• Magnitude

  • E as a force per unit charge
  • $E=$$F/Q$
  • Magnitude of E in a uniform field 
  • $E=$$V/d$
  • $W=$$QEd$
• Electric potential difference - work done per positive unit charge to move a positive test charge from infinity to that point

  • Work done against field lines when moving to infinity
  • W=QV
  • Field is always attractive
  • Potential is zero at infinity
  • Absolute electric potential - potential energy per unit charge
  • All points in an electric field have an absolute potential
  • Depends on how far it is from the charge
• Equipotentials

  • Equipotentials - positions of constant potential in an electric field
  • Always meet field lines at a right angle 
  • No work is done by the field moving a charge along the equipotential
  • Equipotential surface - surface with constant value of potential at all points on the surface
  • No work is done moving a charge along the surface
• Electric potential-distance graph

  • Potential gradient - the rate of change of electric potential per unit distance in the direction of the field
  • $V=$$Q/4\pi\epsilon_0r^2$
  • Electric potential in a radial field
  • $V=$$(1/4\pi\epsilon_0)*$$(Q/r)$
  • Electric field strength
  • E=-V/r
  • Direction of field strength opposes direction of increasing potential

  
• Field-distance graph

  • Area = potential difference
  • E=Q40r2     E∝1r2
  • Area under E-r graph between two points is the potential difference between them