• A field can be defined as

A region in which an object will experience a force, such as gravitational or electrostatic, at a distance

• A gravitational field can be defined as:

The gravitational force per unit mass exerted on a point mass

• An electrostatic field can be defined as:

The electric force per unit charge exerted on a small positive test charge

• Electric field strength,?E, and gravitational field strength,?g, therefore, have very similar equations
  • Despite a few differences, they are analogous to one another in many ways
• In both cases, the nature of the test object is as follows:
  • Gravitational fields:?small mass,?m
  • Electrostatic fields:?small positive charge,?q

Uniform Fields

• A gravitational field is a region of space in which objects with mass will experience a force
• The gravitational field strength can be calculated using the equation:

• Where:
  • g?= gravitational field strength (N kg-1)
  • F?= gravitational force on the mass (N)
  • m?= mass (kg)

• The direction of the gravitational field is always directed?towards?the centre of the mass
  • Gravitational forces are?always attractive?and cannot be repulsive

• An electric field is a region of space in which an electric charge will experience a force
• The electric field strength can be calculated using the equation:
• Where:
  • E?= electric field strength (N C-1)
  • F?= electrostatic force on the charge (N)
  • Q?= Charge (C)
• It is important to use a?positive?test charge?in this definition, as this determines the?direction?of the electric field
• The electric field strength is a?vector?quantity, it is always directed:
  • Away?from a positive charge
  • Towards?a negative charge
• Opposite charges?(positive and negative)?attract?each other
• Conversely,?like charges?(positive-positive or negative-negative)?repel?each other
• The magnitude of the electric field strength in a?uniform?field between two charged parallel plates is defined as:

• Where:
  • E?=?electric field strength?(V m-1)
  • V?= potential difference between the plates (V)
  • d?= separation between the plates (m)

• The electric field strength is now defined by the units?V m–1
  • Therefore, the units V m–1?are equivalent to the units?N C–1

• The equation shows:
  • The greater the?voltage?(potential difference) between the plates, the?stronger?the field
  • The greater the?separation?between the plates, the?weaker?the field

• This equation?cannot?be used to find the electric field strength around a?point charge?(since this would be a radial field)
• The direction of the electric field is from the plate connected to the?positive?terminal of the cell to the plate connected to the?negative terminal

The E field strength between two charged parallel plates is the ratio of the potential difference and separation of the plates

• Note:?if one of the parallel plates is?earthed, it has a voltage of 0 V

Radial Fields

• A point charge or mass produces a?radial?field
  • A charged sphere also acts as a point charge
  • A spherical mass also acts as a point mass

• Radial fields always have an?inverse square law?relationship with distance
  • This means the field strength decreases by a factor of?four?when the distance?r?is?doubled

• The gravitational force?FG?between two masses is defined by:Gravitational vs Electrostatic Forces

• The similarities and differences between gravitational and electrostatic forces are listed in the table below:

Comparing G and E Fields

• The key similarities are:
  • The magnitude of the gravitational and electrostatic force between two point masses or charges are?inverse square law?relationships
  • The field lines around a?point mass?and?negative point charge?are identical
  • The field lines in a?uniform?gravitational and electric field are identical
  • The?gravitational field strength?and?electric field strength?both have a 1 / r2?relationship in a?radial field
  • The?gravitational potential?and?electric potential?both have a 1 /?r relationship
  • Equipotential surfaces?for both gravitational and electric fields are?spherical?around a point mass or charge and?equally spaced?parallel lines in uniform fields
  • The work done in each field is either the product of the?mass?and change in potential or?charge?and change in potential

• The key differences are:
  • The gravitational force acts on particles with?mass?whilst the electrostatic force acts on particles with?charge
  • The gravitational force is?always?attractive whilst the electrostatic force can be attractive?or?repulsive
  • The gravitational potential is?always?negative whilst the electric potential can be either negative?or?positive

Step 1: Write down the known values

• • Potential difference,?V?= 7.9 kV = 7.9 × 103?V
  • Distance between plates,?d?= 3.5 cm = 3.5 × 10-2?m
  • Charge,?Q?= 2.6 × 10-15?C

Step 2: Calculate the electric field strength between the parallel platesExam Tip