Electric Field Lines (HL IB Physics)

• 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, this means that
  • The electric field strength is constant at all points in the field
  • The force on a test charge has the same magnitude and direction at all points in the field

• In a radial electric field, the field lines spread out with distance, this means that
  • The field lines are equally spaced as they exit the surface of the charge
  • However, the radial separation between the field lines increases with distance
  • Therefore, the magnitude of electric field strength and the force on a test charge decreases with distance

Electric Field around a Point Charge

• Around a point charge, the electric field 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, but the strength of the field decreases with distance
  • 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 (whether solid or hollow) becomes charged:
  • Repulsive forces between isolated point charges cause them to become evenly distributed across the surface of the sphere
  • The isolated point charges will either be an excess of negative charges (electrons) or positive charges (protons)

• The resulting electric field around the sphere is the same as it would be if all the charges were placed at the centre
  
  • This means that a charged conducting 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

• Field lines are always perpendicular to the surface of a conducting sphere
  • This is because the field lines show the direction of the force on a charge
  • If the lines were not perpendicular, that would mean there must be a parallel component of the electric force acting
  • This would cause charges on the surface of the conductor to move
  • If this happens, electric repulsion causes the charges to rearrange themselves until the parallel component of the force reduces to zero

• As a result of the perpendicular field lines, the electric field is zero at all points inside the sphere
  • This is because the forces on a test charge inside the sphere would cancel out

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

• The spacing, or density, of field lines, represents the strength of an electric field
  
  • A stronger field is represented by the field lines which are closer together
  • A weaker field is represented by the field lines which are further apart

Strength of a Uniform Field

• The strength of a uniform electric field, such as between two parallel plates, depends on the size of the potential difference between them

• When a higher potential difference is applied across the plates:
  • The density of the field lines is higher
  • The electric field is stronger
  • The force that acts on a test charge in the field is greater

• When a lower potential difference is applied across the plates:
  
  • The density of the field lines is lower
  • The electric field is weaker
  • The force that acts on a test charge in the field is lower

The greater the potential difference, the stronger the electric field and the greater the density of the field lines between the plates

• In a uniform field, the field lines will always be equally spaced, but the spacing will increase or decrease depending on the field strength

Strength of a Radial Field

• Since electric field strength decreases with distance from a point charge, radial fields are considered to be non-uniform
• The strength of a radial electric field depends on
  • The magnitude of the charge
  • The distance between the charge and a point

The greater the magnitude of a point charge, the stronger its electric field and the greater the density of the field lines around it

• Sphere A (from the diagram) has the lowest density of field lines, which means it has
  • The weakest electric field
  • The smallest magnitude of charge at its surface

• Sphere C (from the diagram) has the highest density of field lines, which means it has
  • The strongest electric field
  • The greatest magnitude of charge at its surface

• The shape of a radial field occurs because field lines must be perpendicular to any conducting surface
  • Therefore, electric field lines are equally spaced at the surface of a point charge