Question

Why is force inversely proportional to distance squared?

Answer 1

In general, the force is defined by the ratio of the work done and displacement of the object due to the applied force. But some forces related to attraction or repulsion between the two objects are directly proportional to the product of their masses and inversely proportional to the square of the distance between them. These kinds of forces have to be known and by determining their characteristics the answer can be found.

Complete step by step answer:
The gravitational force and electrostatic force are directly proportional to the product of the masses or charges of the objects and the square of their distance.
The gravitational force is given by, $F = G\dfrac{{{m_1}{m_2}}}{{{r^2}}}$
${m_1},{m_2}$ are the masses of the objects and $r$ is the distance between them.
The electrostatic force or field intensity is given by, $F = k\dfrac{{{q_1}{q_2}}}{{{r^2}}}$
${q_1},{q_2}$ are the charges and $r$ is the distance between them.
These forces maintain the inverse-square law. The law states that a given physical quantity (like illumination) varies inversely with the distance from the source as the square of the distance.
The forces work in all directions from the point source in a uniform manner. It maintains the law of conservation of the energy over the entire surface circumference of the point object. The surface that surrounds it is a sphere. The area of the sphere is given by $4\pi {r^2}$ , where $r$ is the radius of the sphere that is taken as the distance. Hence, the force decreases as the square of the distance.

Note:
Light intensity reduces with distance from the source to the sink or receiver. The rate of the reduction is in proportion to the square of the separation between the emitter and the receiver. This is called the Inverse Square Law. This law for electromagnetic radiation defines that the intensity of light is inversely proportional to the distance squared from the source of radiation.
It can come to mind that the Inverse Square Law is analogous to a volume knob on a speaker system, the intensity is turned down, without affecting the pitch of the music.
The Inverse Square Law does not affect the wavelengths of the emitted light from the surface of the source (such as the Sun), hence, the shape and position of the curve do not change from left to right. but, a change in distance between the emitting and incident surfaces will displace the curve directly up or down.