Electric fields

• Fields --> Regions in which an object will experience a force at a distance
• • A electric field is created by charged objects. Other charged objects in this electric field will experience a force
  • Electrons & protons are charged particles. Both create electric fields & so affect each other
• Electric field strength --> The electric field strength of an electric field at a point in space is defined as the force experienced per unit positive charge at that point
• E = F/Q

  • Electric field strength is a vector quantity - it has direction
  • The direction of the electric field at a point is the direction in which a positive charge would move when placed at that point
  • Electric fields point away from positive charges & towards negative charges
• • Electric field lines can map electric field patterns
  • The arrow on an electric field line show the direction of the field
  • Electric field lines are always at right angles to the surface of a conductor
  • Equally spaced, parallel electric field lines represent a uniform field - one in which the electric field strength is the same everywhere
  • Closer electric field lines represent greater electric field strength
• Electrostatic forces:

  • Coulomb's law --> Any 2 point charges exert an electrostatic ( electrical) force on each other that is directly proportional to the product of their charges & inversely proportional to the square of the distance between them
• Coulomb's law:

  • F is directly proportional to Qq
  • F is directly proportional to 1/r^2
  • F = k ( Qq/ r^2 )
  • k is the constant of proportionality. This constant can be written in terms of permittivity of free space E0
• F = Qq / 4piE0r^2
• Radial fields:

  • A metal sphere with charge +Q, produces a radical field, the speraration between 2 adjacent electric field lines increases with the distance from the centre of the sphere
  • The electric field strength decreases as you move further away from the centre of the sphere
  • E = Q / 4piE0r^2
• • Masses always produce an attractive field
  • Charges can create both attractive & repulsive fields
• Electric field between 2 parallel plates:

  • 2 oppositely charged parallel plates produce a uniform electric field in the region between the plates
  • The electric field strength E between the plates is uniform
  • It experiences a constant force F given by F=EQ
  • The charge will gain energy as it moves from the positive plate to the negative plate
  • VQ = (EQ)d
  • E = V/d --> only works for parallel plates
  • 1NC^-1 = 1Vm^-1
• Parallel plate capacitor:

  • The capacitance of the parallel plate capacitor depends on the separation,d between the plates the area A of overlap between the plates, and the insulator used between plates
  • The capacitance is proportional to the the area
  • Capacitance is inversely proportional to the separation between the plates
  • C = E0A/d
• Permittivity = relative permittivity x permittivity of free space
• Acceleration:

  • The electron experiences a constant electrostatic force because of the uniform electric field between the plates so it has constant acceleration
  • E = V/d
  • Work done on the electron = Vq = Ve
• • For a charged particle moving in an electric field, for the horizontal motion:
  • There is no acceleration, hence the horizontal velocity Vh of the particle remains constant with velocity V
  • The time t spent in the field is given the equation t = L/V
• For the vertical motion:

  • The vertical acceleration a of the particle is given by the equation a= F/m = EQ/m
  • The initial vertical velocity u=0
  • The final vertical component of the velocity v as the particle exits the field is given by the equation : V = u + at = 0 + EQ/m x L/V = EQL/mv
• • Charged particles can also store energy
  • The charges repel each other so you have to do work to decrease the separation between the charges
  • All the work done is stored as electrical potential energy
• • The total work done to bring the particle from infinity to a separation r is the total area under the graph
  • The total work done is the same as the electric potential energy E
  • E = Qq / 4pi x echelon x r
• • If one of the particles has a negative charge, then the value for E will also be negative
  • The force between the particles will be attractive
  • The magnitude of E represents the external energy required to completely separate the charged particles to infinity
• Electric potential:

  • The electric potential V at a point is defined as the work done per unit charge in bringing a positive charge from infinity to the that point
  • V = E / q = Q/ 4pi x echelon x r
  • Electric potential difference is the work done per unit charge between 2 points around the particle of charge Q
• • A capacitor is device that stores charge
  • An isolated, charged sphere of radius R also stores charge
  • C = Q /V