IB DP Physics: HL复习笔记10.1.1 Gravitational & Electrostatic Fields

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

  • 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

7.4.4-Electric-field-between-two-plates

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

7.4.7-G-Fields-v-E-Fields-Table-1

7.4.7-G-Fields-v-E-Fields-Table-3

  • 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 platesExam 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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