DP IB Physics: HL

Revision Notes

Syllabus Edition

First teaching 2014

Last exams 2024

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10.1.1 Gravitational & Electrostatic Fields

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Gravitational & Electrostatic 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:

F i e l d space s t r e n g t h space equals space fraction numerator f o r c e space a c t i n g space o n space a space t e s t space o b j e c t over denominator s i z e space o f space t e s t space o b j e c t 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 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:
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

  • The magnitude of the electric field strength in a uniform field between two charged parallel plates is defined as:

E space equals space V over d

  • 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 m1 
    • 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

Electric field between two plates, downloadable AS & A Level Physics revision notes

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:

F subscript G equals fraction numerator G m subscript 1 m subscript 2 over denominator r space 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 m-1) = (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 / 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

Worked example

Two parallel metal plates are separated by 3.5 cm and have a potential difference of 7.9 kV.

Calculate the electric force acting on a stationary charged particle between the plates that has a charge of 2.6 × 10-15 C.

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 plates

E space equals space V over d space equals space fraction numerator 7.9 cross times 10 cubed over denominator 3.5 cross times 10 to the power of negative 2 end exponent end fraction space equals space 2.257 space cross times space 10 to the power of 5 space end exponent space straight V space straight m to the power of negative 1 end exponent

Step 3: Write out the equation for electric force on a charged particle

F space equals space Q E

Step 4: Substitute electric field strength and charge into electric force equation

F space equals space Q E space equals space left parenthesis 2.6 space cross times space 10 to the power of negative 15 end exponent right parenthesis space cross times space left parenthesis 2.257 space cross times space 10 to the power of 5 right parenthesis space equals space 5.87 space cross times space 10 to the power of negative 10 space end exponent straight N space equals space 5.9 space cross times space 10 to the power of negative 10 end exponent space space straight N space left parenthesis 2 space straight s. straight f. right parenthesis

Exam Tip

Remember to use the correct equation depending on whether there is a uniform or radial field.

For electric fields:

  • Uniform fields: parallel plates / capacitors
  • Radial fields: around point charges

For gravitational fields:

  • Uniform fields: near the Earth's surface
  • Radial fields: around masses (e.g. planets and moons)

You should be able to tell the type of field from the field lines. Uniform fields have equally spaced, parallel field lines.

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