IB DP Physics: HL复习笔记10.1.2 Gravitational & Electrostatic Field Lines

Gravitational Field Lines

• The direction of a gravitational field is represented by gravitational field lines
• The gravitational field lines around a point mass are radially inwards
• The gravitational field lines of a uniform field, where the field strength is the same at all points, is represented by equally spaced parallel lines
  • For example, the fields lines on the Earth’s surface

Gravitational field lines for a point mass and a uniform gravitational field

• Radial fields are considered non-uniform fields
  • The gravitational field strength g is different depending on how far you are from the centre
• Parallel field lines on the Earth’s surface are considered a uniform field
  • The gravitational field strength g is the same throughout

Point Mass Approximation

• For a point outside a uniform sphere, the mass of the sphere may be considered to be a point mass at its centre
  • A uniform sphere is one where its mass is distributed evenly
  • The gravitational field lines around a uniform sphere are therefore identical to those around a point mass

• An object can be regarded as point mass when:

A body covers a very large distance as compared to its size, so, to study its motion, its size or dimensions can be neglected

• An example of this is field lines around planets

Gravitational field lines around a uniform sphere are identical to those on a point mass

• Radial fields are considered non-uniform fields
  • So, the gravitational field strength g is different depending on how far an object is from the centre of mass of the sphere

Representing Electric Fields

• 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

• A radial field spreads uniformly to or from the charge in all directions
  • e.g. the field around a point charge or sphere

• 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

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 an attractive force, the field lines will look similar to the negative point charge, whilst electric field lines can be in either direction

• 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 and 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 represented by the spacing of the field lines:
  • A stronger field is represented by the field lines which are closer together
  • A weaker field is represented by the field lines which are  further apart

• The electric field lines are directed from the positive to the negative plate

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

• A radial field is considered a non-uniform field
  • Electric field strength E varies with distance from a charged particle

• Arrows (representing force on a positive test charge) point from the positive charge to the negative charge