Using Field Lines & Equipotential Diagrams
- The direction of electric fields is represented by electric field lines
- Electric field lines are directed from positive to negative
- Therefore, the field lines must be pointed away from the positive charge and towards the negative charge
- Hence, field lines show the direction of force on a positive test charge
Representing Radial Fields
- A radial field spreads out from a spherical charge in all directions
- e.g. the 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
Radial electric field lines point away from a positive charge and point towards a negative charge
- This shares many similarities to radial gravitational field lines around a point mass
- Since gravity is only attractive, the field lines will look similar to the negative point charge, directed inward
- However, electric field lines can be in either direction
- The electric field strength in a radial field follows an inverse square law
- This means the field strength varies with distance r by 1 / r2
Representing Uniform Electric Fields
- A uniform electric field has the same electric field strength throughout the field
- For example, the field between oppositely charged parallel plates
- This is represented by equally spaced field lines
- This shares many similarities to uniform gravitational field lines on the surface of a planet
- A non-uniform electric field has varying electric field strength throughout
- The strength of an electric field is determined by the spacing of the field lines:
- A stronger field is represented by the field lines closer together
- A weaker field is represented by the field lines further apart
The electric field between two parallel plates is directed from the positive to the negative plate. A uniform E field has equally spaced field lines
- The electric field lines are directed from the positive to the negative plate
- The electric field strength in a uniform field is given by the equation E = V / d
- Hence, E proportional to the potential difference V between the plates
- E is inversely proportional to the distance d between the plates
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)
- The potential gradient is defined by the equipotential lines
Equipotential lines in a radial field are circles, showing lines of equal potential around a charge. They intersect radial field lines at 90°
Equipotential lines in a uniform field are straight lines. They too intersect uniform field lines at 90°
Worked example
Sketch the electric field lines between the two point charges in the diagram below.
- Electric field lines around point charges are radially outwards for positive charges and radially inwards for negative charges
- The field lines must be drawn with arrows from the positive charge to the negative charge
- In a radial field (eg. a point charge), the equipotential lines:
- Are concentric circles around the charge
- Become further apart further away from the charge
- In a uniform field (eg. between charged parallel plates), the equipotential lines are:
- Horizontal straight lines
- Parallel
- Equally spaced
- No work is done when moving along an equipotential line or surface
- Work is only done when moving between equipotential lines or surfaces
- This means that an object travelling along an equipotential doesn't lose or gain energy and ΔV = 0
Exam Tip
Always label the arrows on the field lines! The lines must also touch the surface of the source charge or plates.