OCR A Level Physics

Revision Notes

6.3.6 Electric vs Gravitational Fields

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Electric Fields vs Gravitational Fields

  • 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

  • Fields can be described in terms of field strength, which is defined as:

Field strength = fraction numerator force space acting space on space straight a space test space object over denominator size space of space test space object end fraction

  • 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:
g equals F over m
  • Where:
    • g = gravitational field strength (N kg−1)
    • F = gravitational force on the charge (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:
E equals F over Q
  • 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

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:

F subscript G equals fraction numerator G m subscript 1 m subscript 2 over denominator r squared end fraction

  • Where:
    • FG = gravitational force between two masses (N)
    • G = Newton’s gravitational constant
    • m1m2 = two points masses (kg)
    • r = distance between the centre of the two masses (m)
  • The electric field strength E at a distance r due to a point charge Q in free space is defined by:

E equals fraction numerator Q over denominator 4 pi epsilon subscript 0 r squared end fraction

  • Where:
    • Q = the point charge producing the radial electric field (C)
    • r = distance from the centre of the charge (m)
    • ε0 = permittivity of free space (F m1) = (epsilon subscript 0 equals 8.85 cross times 10 to the power of negative 12 end exponent space F space m to the power of negative 1 end exponent)
  • This equation shows:
    • The electric field strength in a radial field is not constant
    • As the distance, r, from the charge increases, E decreases by a factor of 1/r2

Gravitational vs Electrostatic Forces

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

Comparing G and E Fields 

G Fields v E Fields Table 1, downloadable AS & A Level Physics revision notesG Fields v E Fields Table 2, downloadable AS & A Level Physics revision notesG Fields v E Fields Table 3, downloadable AS & A Level Physics revision notes

  • 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 / r 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

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