Gravitational field
Section: Gravitational Fields | Syllabus: Cambridge AS Level Physics 9702
Concept of a Field Physicists use the concept of a field of force to describe non-contact interactions, such as objects falling toward Earth, magnets attracting each other, and electric charges interacting.
Key Principle Masses, charges, and magnets create fields in the space around them. Any object placed in those fields may experience a force. A field is represented by a vector having both magnitude and direction.
Note on Reciprocity: Gravity is a two-way street. While Earth attracts you, you attract the Earth with a force equal in magnitude but opposite in direction. Gravitational Field Strength (g) The gravitational field at a point is defined as the gravitational force per unit mass at that point.
It is a vector quantity. g = F/m Units: N kg^-1 (Equivalent to m s^-2). g as Acceleration of Free Fall By comparing Newton's Second Law (F = ma a = F/m) with the field definition (g = F/m), we see that g is numerically equivalent to the acceleration of free fall .
At Earth's surface, g = 9.81 N kg^-1 = 9.81 m s^-2. Because F m, the ratio F/m is constant for all objects at a specific location. Therefore, all objects in the same field have the same acceleration, regardless of mass.
Worked Example: Force on a Rock Question: Calculate the force of gravity on a rock of mass 1500 g (1.5 kg) at Earth's surface. Solution F = mg = 1.5 kg × 9.81 N kg^-1 = 14.7 N. Field Lines and Patterns Field lines show the direction of force on a mass.
The Earth's field is a radial field because the lines point towards the Earth's centre. Figure 13.1: The Earth's Radial Field Show field lines incident on the Earth's surface at 90°. Lines converge toward the centre.
As distance increases, lines get further apart, indicating the field is becoming weaker. Uniform Field Approximation On a small scale (e.g., inside a room), the field lines appear parallel and equidistant.
In this case, Earth's field is considered uniform , meaning g is constant for small changes in height.
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