Can the magnitude of the displacement vector be more than the distance traveled less than the distant traveled explain

The displacement of a body will always be less than or equal to the distance traveled. It cannot have a value greater than the distance traveled.

Distance is the length of the path traveled by the body, while displacement is the shortest distance between the starting and the ending point.

Consider a body moving from point A to B along the curved path as shown in the diagram. The distance traveled is the length of the curved path from A to B.

The displacement of the body is measured along the straight line drawn from A to B.

It can be seen that the distance traveled is greater than the displacement. The distance traveled will be equal to the displacement if the body travels along the straight line drawn from A to B.

Since the displacement is always the shortest distance between the starting and ending point, it can have a value less than or equal to the distance traveled.

gas and liquid

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.