For IB Physics HL: gravitational field strength is the negative gradient of gravitational potential. In one radial dimension,
For IB Physics HL: gravitational field strength is the negative gradient of gravitational potential. In one radial dimension,
so the magnitude of the field strength is .
Gravitational potential is the work done per unit mass in bringing a small test mass from infinity to a point in a gravitational field. Gravitational field strength is the gravitational force per unit mass at that point.
The general vector relationship is
The potential gradient measures how rapidly potential changes with position. A steeper potential-position graph therefore represents a stronger gravitational field. Its units confirm the relationship:
The negative sign shows that the field points in the direction of decreasing potential. Around an isolated spherical mass, potential increases outward from a negative value toward zero. Therefore, , making : the field points inward.
For a spherical mass, . Differentiating gives , so . This matches Newton's law: the magnitude decreases as , while the negative radial component identifies the inward direction. Equipotential surfaces are perpendicular to field lines because movement along an equipotential produces no potential change and therefore no work per unit mass.
For example, suppose the potential changes from to over an outward distance of :
Hence,
meaning a field strength of directed inward.
For a curved graph, the field at one position comes from the tangent gradient at that point. A steeper tangent means a greater field magnitude.
A common misconception is that the negative sign means the field strength is physically negative. It indicates direction, not a negative magnitude.
This is Additional Higher Level content in D.1 Gravitational fields. When asked to explain the relationship, state the equation, interpret the negative sign, and connect the gradient's magnitude to field strength. On a -against- graph, use the tangent gradient at the specified point, not the potential value itself.