Force fields

A body can experience a force without touching the object producing it. A force field describes the region around a source where such a non-contact interaction can occur. Whether a body experiences a force depends on its properties and the type of field.

Different interactions have different sources:

• A gravitational field arises from mass and acts on other masses.
• An electrostatic field arises from static electric charge and acts on other charges.
• A magnetic field can arise from moving charges. Magnetic forces can act between moving charges.

Field direction and force direction

At each point, a field has a magnitude and a direction. It can therefore be represented by a vector: an arrow whose direction shows the field direction and whose length represents the field magnitude.

To work out the force on a body, both the field and the nature of the interaction must be considered. The force is not always in the same direction as the field vector:

• In a gravitational field, the force on a mass is in the field direction.
• In an electrostatic field, the field direction is defined as the force direction on a positive charge. A negative charge experiences a force in the opposite direction.
• In a magnetic field, the force on a moving charge depends on its charge and direction of motion as well as the field direction. The force is not generally along the field direction.

Gravitational and electrostatic field comparison

Gravitational and electrostatic forces both act at a distance. For point sources, the magnitude of each force follows an inverse-square law: it is proportional to $$1/r^2$$, where $$r$$ is the separation between the sources. If the separation doubles, the force becomes one-quarter as large.

The forces differ in their direction. Gravity between two masses is always attractive. Electrostatic force is attractive between unlike charges but repulsive between like charges.

Comparing field lines

A field describes the force a test body would experience at each point. Field lines represent the direction of a field: the direction of a line at a point is the field direction there. Lines drawn closer together indicate a stronger field relative to regions where they are farther apart.

• The gravitational field direction is the direction of the force on a test mass. Around a point mass, field lines point towards the mass.
• The electric field direction is the direction of the force on a positive test charge. Around a positive point charge, field lines point away from the charge; around a negative point charge, they point towards it.

Comparing potentials and equipotential surfaces

Both fields can also be described using potential. Gravitational potential is gravitational potential energy per unit mass. Electric potential is electric potential energy per unit charge.

An equipotential surface joins points with the same potential. Moving a test body along such a surface does not change its potential energy, so the field does no work on it. Field lines are perpendicular to equipotential surfaces: if a field had a component along the surface, it would do work during a displacement in that direction.