How does field strength vary with distance?

Field strength decreases as the distance from the source increases, following an inverse square law.

In more detail, the concept of field strength and its variation with distance is a fundamental principle in physics. It applies to various types of fields, including gravitational, electric, and magnetic fields. The inverse square law states that the strength of these fields is inversely proportional to the square of the distance from the source. This means that as you move away from the source, the field strength decreases rapidly.

For instance, consider a point source that emits a field in all directions uniformly. At a certain distance from the source, the field spreads out over the surface of a sphere centred on the source. The surface area of this sphere is proportional to the square of the radius (which in this case is the distance from the source). Therefore, the field strength, being spread over this area, decreases with the square of the distance.

This principle is mathematically represented as F ∝ 1/r², where F is the field strength and r is the distance from the source. This equation tells us that if you double the distance from the source (r), the field strength (F) will be reduced to a quarter of its original value. Similarly, if you triple the distance, the field strength will be reduced to a ninth of its original value.

However, it's important to note that this law assumes an ideal point source with no obstacles or other sources nearby. In real-world situations, other factors can influence the field strength. For example, in an electric field, the presence of other charges can affect the field strength. Similarly, in a gravitational field, the presence of other masses can alter the field strength. Therefore, while the inverse square law provides a fundamental understanding of how field strength varies with distance, it's always essential to consider the specific context and conditions.