Question

Potential difference between two points in an electric field is:
(A) A scalar quantity
(B) A vector quantity
(C) A tensor quantity
(D) None of these

Answer 1

Hint: For distinguishing between a vector and a scalar quantity, we check whether it follows rules of vector addition. If it follows the rules of vector addition, then it is a vector quantity, otherwise it is a scalar quantity.

Complete step-by-step solution
We know that the vectors are the quantities which are associated with the magnitude and the direction. So it can change by the change either of the magnitude or the direction.
But scalars are associated only with the magnitude. No direction is defined for the scalar quantities. So it cannot change with the direction. Therefore its magnitude is independent of the direction.
We know that the resultant electric field at a particular point, in a region where there are multiple fields present, is obtained by the vector addition of all the electric field vectors. So the electric field is a vector quantity.
But we know that the potential difference between two points in an electric field is independent of the path chosen for traversing from one point to the other. It only depends on the end points. Let us consider three points A, B, and C in an electric field. Let ${V_{AB}}$ be the potential difference between the points A and B, and ${V_{BC}}$ be the potential difference between the points B and C. For obtaining the potential difference between the points A and C, we algebraically add the potential differences ${V_{AB}}$ and ${V_{BC}}$. There is no vector addition involved.
So the potential difference between two points in an electric field is a scalar quantity.
Hence, the correct answer is option A.

Note
A tensor quantity is basically a multidimensional array. They are represented in the form of matrices. Both the scalars and vectors are the categories of the tensor. The scalar is a tensor having zero dimensions, while the vectors are the one dimensional tensors.