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Energy and Fields overview

Topic 3 of 6

Field strength, patterns and force

A field describes how a suitable body may experience a force at each position. It belongs to the source arrangement and exists whether or not a test body is currently placed there.

Define field strength at a point

Gravitational field strength, g
The gravitational force per unit mass on a mass placed at that point. Its direction is the force direction, and its unit is N/kg.
Electric field strength, E
The electric force per unit charge on a positive test charge placed at that point. Its direction is the force direction on that positive charge, and its unit is N/C.
g = gravitational force / mass
E = electric force / positive test charge

Use a sufficiently small test charge so that it does not substantially disturb the source arrangement. A smaller test mass or charge experiences a smaller force in the same field; that alone does not mean the field has become weaker.

Worked field-strength ratios

A 0.200 kg mass experiences a gravitational force of 1.962 N downward:

g = 1.962/0.200 = 9.81 N/kg downward

A positive 2.0 × 10-7 C charge experiences an electric force of 4.0 × 10-4 N right:

E = (4.0 × 10-4)/(2.0 × 10-7)
= 2.0 × 103 N/C right

These supplied forces and test-body quantities determine the force ratios at the point. They do not by themselves describe the instrument method for measuring a very small charge.

When gravity is the only force, F = ma and gravitational force = mg give a = g. This connects g in N/kg with free-fall acceleration in m/s2. Determining force per unit mass and timing a falling body's motion are different measurement methods, even when they give the same numerical value for g.

Electric field strength is also expressed in the equivalent unit V/m. Its connection with potential difference across a distance uses a uniform-field model. Keep the present definition, force per unit positive charge, clear. The letter E can mean field strength or energy; its definition and units distinguish them.

Interpret field lines

Field lines show local field direction, not compulsory trajectories

The source arrangement creates the field even when no test body is drawn. These are schematic field patterns, not a numerical scale of field strength.

Approximately uniform gravitational field

Approximately uniform gravitational fieldIn a small region near Earth, the field lines are parallel, equally spaced and directed down. Each green arrow gives the local gravitational field direction. The drawn ground is not an equipotential construction or a scale for field strength.g downwardA small region near Earth's surface

Radial gravitational field outside a spherical mass

Radial gravitational field outside a spherical massOutside a spherically symmetric source mass, straight radial lines point inward towards its centre. Eight representative lines lie in this drawing plane. They do not cross outside the source. Their closer spacing near the source indicates stronger field qualitatively, not a numerical field-strength scale.MField inward outside the source mass

Uniform electric field between parallel plates

Uniform electric field between parallel platesThe left plate is positive and the right plate negative. Away from their edges, representative field lines are straight, parallel, equally spaced and directed from the positive plate to the negative plate. No fringing region or test-charge trajectory is shown.+-+-+-+-+-E from positive to negativeUniform model away from plate edges

Radial electric field of a positive point source

Radial electric field of a positive point sourceThe positive point source has radial field lines directed outward. The drawn source symbol has an arbitrary size. Field lines do not cross outside it and are not paths that every moving particle must follow.+QField outward from the positive source

Radial electric field of a negative point source

Radial electric field of a negative point sourceThe negative point source has radial field lines directed inward. The drawn source symbol has an arbitrary size. Field arrows are defined using force on a positive test charge; a negative test charge would experience force in the opposite direction.-QField inward towards the negative source
Uniform and radial patterns represent field direction at positions. Gravitational arrows point towards the source mass; electric arrows point away from a positive source and towards a negative one.
  • Uniform gravitational field: in a small region near Earth's surface, lines are approximately parallel, equally spaced and downward.
  • Radial gravitational field: outside a spherically symmetric mass, lines point towards its centre.
  • Uniform electric field: between parallel plates, away from their edges, lines point from the positive plate to the negative plate.
  • Radial electric fields: lines point outward from a positive point charge and inward towards a negative point charge.

The tangent to a line gives the local field direction. Closer lines indicate a stronger field under a consistent drawing convention. Lines cannot cross where the field has a defined direction, because one point cannot have two different resultant field directions. They are representations, not physical strings.

A positive mass experiences force along g. For a charge, F = qE with the charge's sign included: a positive charge has force along E; a negative charge has force opposite E. A field line is not a compulsory trajectory. The body's velocity may point in a different direction from the force.