Question

Define Displacement vector.

Answer 1

Hint: Displacement vector can be thought of as the shortest path between the initial and final positions of any body that is moving or has been in motion earlier and thus, has displaced from its initial position. You can define it very easily now.

Formulas used:
The magnetic field inside the core of the toroid is given by, $B={\displaystyle \frac{{\mu }_{0}NI}{l}}$ where, ${\mu }_0$ is the permeability of free space, $N$ is the number of turns on the toroid, $I$ is the current through the wire and $l$ is the length of the wire.

Complete step by step solution:
For us to actually define displacement vectors, we first need to discuss position and position vectors.
We can describe the position of a body as a quantity which gives us details about the whereabouts of the body, i.e. where is the body at any particular given time.
On the other hand, position vector can be defined as a vector which tells us the position of the body with reference to a reference point or reference frame, usually taken as the origin of the plane or graph. In actual problems, earth is taken to be the reference frame.
Now that we know about both, position and position vector, we are fully capable of defining displacement and displacement vectors.
Displacement can be thought of as the shortest path or shortest path distance between the initial and final positions of any body that has been in, or is in motion.
Displacement vector is the vector subtraction of the initial position vector of the body from the final position vector of the body. This is the shortest path which is directed from the initial position of the body in motion to the final position of the body.

Note:
An important point at which many students make mistakes is that distance is the actual path travelled by the body, on the other hand, displacement has no concerns about the path chosen to displace from one point to another, it only considers the initial and final position. You are never supposed to confuse between distance and displacement.