Question

Define scalar quantity.

Answer 1

Hint: Initially we have to find the induced emf due to change in the magnetic field, from Faraday’s law. Then draw an analogous circuit from the induced emf and the given resistance per unit length. Apply Kirchhoff's Voltage law to each of the loops ADFEA and FCBEF. Solve the obtained equations.

Complete step by step answer:
Let us first understand two terms – magnitude and direction.
Magnitude is the mathematical entity or simply the numerical value which gives the size of the object. It aids to determine whether a quantity is larger or smaller compared to every other numerical value. But this comparison is only valid when the quantities belong to the same kind. Magnitude can be a real or a complex number.
Direction indicates the course or the path taken by the object.
Generally based on magnitude and direction, quantities in physics are distributed into two kinds. They are vectors and scalars.
The vectors are the quantities which have magnitude and direction.
In physics, a scalar quantity is described as a quantity that only has magnitude.
Scalar quantities can be divided into two kinds based on their use as tensors. They are relativistic and non-relativistic scalars.
Best examples of scalars are mass (m), charge (q), current (i), speed(s), etc.,
The relativistic scalars can be used as rank zero tensors in Euclidean space. Examples include scalars like speed, mass, distance, charge, etc.,
The non-relativistic scalars are those which can represent the quantity only at a single point. One such example is temperature.
The most common way to distinguish a scalar quantity from a vector quantity is by looking out for a right arrow or a straight line over the variable. This arrow represents that the variable has a direction, thus it is a vector. For example, $\vec v$or $\bar v$ denotes the velocity which is a vector. In scalar quantities, any such notation is absent. $

Note:
Multiplication of two vectors, by dot product, results in a scalar. For example, $W = \vec F \cdot \vec s$, here work done is a scalar which is a dot product of the two vectors, force, displacement, etc.
Both the vectors and scalars are always accompanied by units.
A scalar and vector addition or subtraction is not possible.