Electric Fields

• Where $\epsilon_0$is the permittivity of free space, $Q_1 +$$Q_2$are charges, r is the distance between charges.
• Coloumb's Law:

  • States that the magnitude of the force between two point charge in a vacuum is directly proportional to the product of their charges.
  • Also that they are inversely proportional to the square of the distance between the charges.

  Air can be treated as a vacuum and charge is assumed to act at the centre of the sphere.

  $F =$$\frac{1}{4\pi \epsilon_0}\frac{Q_1 Q_2}{r^2}$
• The magnitude of electrostatic forces between subatomic particles is much greater than gravitational forces, as the masses are incredibly small whereas charges are much greater.
• Electric Field Strength:

  • The force per unit charge experienced by an object in an electric field.
  • Equations for uniform field:
  • $E=$$\frac{F}{Q}$
  • $E=$$\frac{V}{d}$
  • Equation for radial field:
  • $E=$$\frac{1}{4\pi \epsilon_0}\frac{Q}{r^2}$

  
• Field Lines:

  • The field lines show the direction of the force acting on a positive charge.
  • A uniform field exerts the same electric force everywhere in the field.
  • Force in a radial field depends on the distance between the two charges.
  • Work done in a field:
  • $Work=$$Q\Delta V$
• Absolute Electric Potential:

  • The potential energy per unit charge of a positive point charge at that point in the field.
  • Absolute magnitude is greatest at the surface of a charge.
  • Value of potential can be found using:
  • $V=$$\frac{1}{4\pi \epsilon_0}\frac{Q}{r}$
• Charge affecting potential:

  • Whether the value of potential is negative or positive depends on sign of charge (Q).
  • When charge is positive, potential is positive and charge is repulsive.
  • When charge is negative, potential is negative and the force is attractive.
• Electric Potential Difference ($\Delta V$):

  • The energy needed to move a unit charge between two points.
  • Work done in moving a charge across a potential different to the product of potential difference and charge.
  • $\Delta W=$$Q\Delta V$
• Equipotential Surfaces in electric fields:

  • Potential on an equipotential surface is the same everywhere so when a charge moves across the surface, no work is done.