# 7.8 Representing Radial & Uniform Electric Fields

## 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

• 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.

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