8.3 Newton’s third law of motion

Third law of motion is different to other two laws of motion in what it describes. This law states about an important characteristic of force rather than the relation between force and motion as described by the first two laws.

Newton’s third law of motion

One body interacts with other body exerting force on each other, which are equal in magnitude, but opposite in direction.

The action and reaction pair acts along the same line. Their points of application are different as they act on different bodies. This is a distinguishing aspect of third law with respect first two laws, which consider application of force on a single entity.

The law underlines the basic manner in which force comes into existence. Force results from interaction of two bodies, always appearing in pair. In other words, the existence of single force is impossible. In the figure below, we consider a block at rest on a table. The block presses the table down with a force equal to its weight (mg). The horizontal table surface, in turn, pushes the block up with an equal normal force (N), acting upwards.

$$N=\mathrm{mg}$$

In this case, the net force on the block and table is zero. The force applied by the table on the block is equal and opposite to the force due to gravity acting on it. As such, there is no change in the state of block. Similarly, net force on the table is zero as ground applies upward reaction force on table to counterbalance the force applied by the block. We should, however, be very clear that these action and reaction force arising from the contact are capable to change the state of motion of individual bodies, provided they are free to move. Consider collision of two billiard balls. The action and reaction forces during collision change the course of motion (acceleration of each ball).

The "action" and "reaction" forces are external forces on individual bodies. Depending on the state of a body (i.e. the state of other forces on the body), the individual "action" or "reaction" will cause acceleration in the particular body. For this reason, book and table do not move on contact, but balls after collision actually moves with certain acceleration.

The scope of this force is not limited to interactions involving physical contact. This law appears to apply only when two bodies come in contact. But, in reality, the characterization of force by third law is applicable to all force types. This requirement of pair existence is equally applicable to forces like electrostatic or gravitational force, which act at a distance without coming in contact.

Let us consider the force between two charges $q_1$ and $-q_2$ placed at a distance "r" apart. The magnitude of electrostatic force is given by :

$$\begin{array}{l}F=\frac{q_1{q}_2}{4\pi {\epsilon }_0{r}^2}\end{array}$$

The charge $q_1$ applies a force $F_{21}$ on the charge $q_2$ and charge $q_2$ applies a force $F_{12}$ on $q_1$ . The two forces are equal in magnitude, but opposite in direction such that :