Representing Radial & Uniform Electric Fields (Edexcel A Level Physics)

Electric field lines

• Field lines are used to represent the direction and magnitude of an electric field
  • In an electric field, field lines are always directed from the positive charge to the negative charge

• In a uniform electric field:
  • the field lines are equally spaced at all points
  • electric field strength is constant at all points in the field
  • the force acting on a test charge has the same magnitude and direction at all points in the field

• In a radial electric field:
  
  • the field lines are equally spaced as they exit the surface of the charge but the distance between them increases with distance
  • the electric field strength decreases with distance from the charge producing the field
  • the magnitude of the force acting on a test charge decreases with distance

Electric field around a point charge

• Around a point charge, the electric field is radial and the lines are directly radially inwards or outwards
  • If the charge is positive (+), the field lines are radially outwards
  • If the charge is negative (-), the field lines are radially inwards

Electric field lines around a point charge are directed away from a positive charge and towards a negative charge

• A radial field spreads uniformly to (or from) the charge in all directions, and the strength of the field is indicated by the spacing of the field lines
  • The electric field is stronger where the lines are closer together
  • The electric field is weaker where the lines are further apart

• This shares many similarities to radial gravitational field lines around a point mass
  • Since gravity is only an attractive force, the field lines will look similar to the negative point charge, whilst electric field lines can be in either direction

Electric field around a conducting sphere

• When a conducting sphere becomes charged, the electric field around it is the same as it would be if all the charge was concentrated at the centre
  • This means that a charged sphere can be treated in the same way as a point charge in calculations

Electric field lines around a charged conducting sphere are similar to the field lines around a point charge

• Note: field lines are always perpendicular to the surface of a conducting sphere

Electric field between two point charges

• For two opposite charges:
  • the field lines are directed from the positive charge to the negative charge
  • the closer the charges are brought together, the stronger the attractive electric force between them becomes

The electric field lines between two opposite charges are directed from the positive to the negative charge. The field lines connect the surfaces of the charges to represent attraction

• For two charges of the same type:
  • the field lines are directed away from two positive charges or towards two negative charges
  • the closer the charges are brought together, the stronger the repulsive electric force between them becomes
  • there is a neutral point at the midpoint between the charges where the resultant electric force is zero

The electric field lines between two like charges are directed away from positive charges or towards negative charges. The field lines do not connect the surfaces of the charges to represent repulsion

Electric field between two parallel plates

• When a potential difference is applied between two parallel plates, they become charged
  • The electric field between the plates is uniform
  • The electric field beyond the edges of the plates is non-uniform

Electric field lines between two parallel plates are directed from the positive to the negative plate. A uniform electric field has equally spaced field lines

Electric field between a point charge and parallel plate

• The field around a point charge travelling between two parallel plates combines
  • the field around a point charge
  • the field between two parallel plates

The electric field lines between a point charge and a parallel plate are similar to the field between two opposite charges. The field lines become parallel when they touch the plate

Equipotential diagrams

• Equipotential lines (2D) and surfaces (3D) join together points that have the same electric potential
• These are always:
  • perpendicular to the electric field lines in both radial and uniform fields
  • represented by dotted lines (unlike field lines, which are solid lines with arrows)
  • an equal distance from the source charge

• Equipotential surfaces can be drawn to represent a fixed electric potential for a number of scenarios, such as
  • for a point charge
  • for two or more charges
  • between two oppositely charged parallel plates

Equipotential surface for a point charge

• In a radial field, such as around a point charge, the equipotential lines:
• are concentric circles around the charge
• become progressively further apart with distance

Equipotential lines for a radial electric field are concentric circles which increase in radius and are perpendicular to the field lines

• If a charged conducting sphere replaced a point charge, the equipotential surface would be the same 

Equipotential surface for multiple charges

• The equipotential surfaces for a dipole (two opposite charges) and for two like charges are shown below:

The equipotential surface for multiple charges can be obtained by drawing curves which are perpendicular to the field lines

• An equipotential surface between two opposite charges can be identified by a central line at a potential of 0 V
  • This is the point where the opposing potentials cancel

• An equipotential surface between two like charges can be identified by a region of empty space between them
  • This is the point where the resultant field is zero

Equipotential lines show that the potential has the greatest value near the charge and decreases with distance

Equipotential surface between parallel plates

• In a uniform field, such as between two parallel plates, the equipotential lines are:
• horizontal straight lines
• parallel
• equally spaced

The equipotential lines for a uniform field are evenly spaced parallel lines which are perpendicular to the field lines

• The spacing between equipotential lines indicates the strength of the electric field
  • This is because they represent potential gradient

• Hence, equally spaced equipotential lines indicate a region of constant electric field strength