E Field - Detailed

• An electric field is defined as a region of space in which a charged particle experiences a force

  • The charged particle could be stationary particle could be stationary or moving, and will experience an electric force in that field
  • All charged particles create their own electric fields, these fields exert an electrostatic force on other charged particles
• Like charges repel, and opposite charges attract
• Repulsive forces decrease with distance
• Electric Field Strength is the force per unit charge acting on a positive test charge at that point
• E = F / Q, where E is electric field strength, F is force and Q is charge
• Since electric field strength is a vector, it is always directed (when drawing lines)

  • Away from a positive charge
  • Towards a negative charge
• All charged particles produce an electric field around then, this field exerts a force on any other charged particle within a range
•  

  Electrostatic force between two charges is defined by Coulomb's Law - The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation
• F = Qq / kr^2

  • When distance double, electrostatic force quarters due to inverse square law
  • If the charges are oppositely charged, then F is negative (attractive force)
  • If the charges are the same charge, then F is positive (repulsive force)
• Electric field strength describes how strong or weak an electric field is at that point

  A point charge produces a radial field
• E = Q/kr^2

  • Electric field strength in a radial field is not constant
  • As distance doubles , E decreases by a quarter due to inverse square law
  • Only works for the field strength around a point charge since it produces a radial field
• Electric field - distance graph

  • Values of E are all positive
  • As distance increases, E decreases due to inverse square law
  • Area under graph is change in electric potential
  • Graph has a steep decline as r increases
• A positive test charge has electric potential energy due to its position in an electric field, which depends on

  1. The magnitude of the charge
  2. The value of the electric potential in the field
• Work is done on a positive test charge to move it from the negatively charged plate to the positively charged plate, hence electric potential energy increases
• Electric potential is the amount of work done per unit of charge

  1. A stronger electric field means the electric potential changes more rapidly with distance
  2. So, the relationship between electric field strength and gradient of electric potential is proportional
  3. If the electric potential changes gradually with distance, the electric field strength is small
• The electric field at a particular point is equal to the gradient of a potential-distance graph at that point
• The potential gradient in an electric field is the rate of change of electric potential with respect to displacement in the direction of the field
• Graph of potential against distance

  • All values are negative/positive for a negative/positive charge
  • As distance increases, potential follows a -1/r for negative and 1/r for positive
  • Gradient of the graph is the value of E at that point
  • Graph has a shallow increase as distance increases
• If the charge is positive/negative the potential decreases/increases with distance
• E = V / d

  • The greatest voltage between the plates, the stronger the field
  • The greater separation between the plates, the weaker the field
• Direction of the electric field is from the positive terminal to the negative terminal
•  

  In order to move a positive charge closer to another positive charge, work must be done to overcome the force of repulsion between them. Therefore, energy is transferred to the charge that is being pushed upon an its potential energy increases
• If the positive test charge is free to move, it will start to move away from the repelling charge, and it's potential energy decreases back to zero
• The electric potential is the work done per unit charge in bringing a positive test charge from infinity to that point
• Positive work is done to move a positive test charge from infinity to a point around a positive charge and negative work is done to move it to a point around a negative charge

  • When a positive test charge moves closer to a negative charge, its electric potential decreases
  • When a positive test charge moves closer to a positive charge, its electric potential increases
• V = Q / kr

  Positive test Charge:

  • As distance from charge decreases, potential increases
  • Due to more work being done on the positive test charge to overcome the repulsive forces

  Negative test Charge:

  • As distance from charge decreases, potential decreases
  • Due to less work being done on the negative test charge since the attractive forces become stronger as it gets nearer to charge
• Around a point charge

  1. If the charge is positive, field lines are radially outwards
  2. If the charge is negative, field lines are radially inwards
•  

  In a uniform field

  1. Lines are equally spaced
  2. Lines a parallel
  3. Horizontal
• Equipotential lines are always perpendicular to the electric field lines and represented by dotted lines, as lines get further apart in a radial field, potential decreases
•  

  No work is done while a charge moves along a equipotential line in a radial field, only when moving between equipotential lines
• Used to store energy in electric circuits, they do this by storing electric charge, which creates a build up of electric potential energy
•  

  They are made in the form of two conductive metal plates connected to a voltage supply, and there is commonly a dielectric between the plates to charge doesn’t flow across them
• Capacitance is the charge stored per unit potential difference, the greater the capacitance the greater the charge stored
• C = Q / V with the unit Farad (F)
• If the capacitor is made of parallel plates, Q is the charge on the plates and V is the potential difference across the capacitor, Q isn't the charge of the capacitor but the charge stored on the plates
•  

  (Capacitance equation shows that) an object's capacitance is the ratio of the charge stored by the capacitor to the potential difference between the plates
• When charging a capacitor, the power supply 'pushes' electrons to one of the metal plates, so it does work on the electrons and electrical energy becomes stored on the plates
• Powers supply 'pulls' electrons off the other metal plate, attracting them to the positive terminal, leaving one side positively charged and the other negatively charged

  • At first, adding more electrons to the negative plate is relatively easy at first since there is little repulsion
  • As the charge of the negative plate increases, the force of repulsion increases therefore a greater amount of work must be done to increase the charge on the negative plate
  • The potential difference across the capacitor increases as the amount of charge increases
• Three equations for energy stored on a capacitor;

  W = 1/2QV

   

  W = 1/2CV^2

   

  W = Q^2/2C
• Potential Difference - Charge graph

  • Used by Q = CV
  • So charge is directly proportional to potential difference
  • Gradient is 1/capacitance
  • Electric potential energy stored in the capacitor is the area under the graph