Question

Potential gradient is a __________.
A. Vector quantity
B. Scalar quantity
C. Conversion factor
D. Constant

Answer 1

Hint: Vector quantities are those quantities which have both direction and magnitude whereas scalar quantities are those which have only magnitude but do not have any direction. We will study the potential gradient and its properties to find whether it is a vector or scale or constant or just a conversion factor.

Complete answer:
We came across many definitions of potential gradient in terms of numerical formula or theoretical concept. Theoretically we can define potential gradient as gradient of potential. It means that whenever there is difference in potential or there is some potential difference between two then for some fixed value then it is known as potential gradient.

Numerically we can say that potential gradient is the potential ration per unit length. Therefore it is the ratio of potential difference and length of conductor. Hence it can be represented as,
Potential Gradient \[{\text{ = - }}\dfrac{{\Delta {\text{V}}}}{{\Delta x}}\]
\[\Delta {\text{V}}\] is the change in potential between two points and \[\Delta x\] is the distance between those two points.

We know that potential is a scalar quantity and according to properties of vector and scalar quantity, we know that the gradient of any scalar quantity gives us a vector quantity. Thus we can say that the gradient of potential will be a vector quantity.

Therefore, the correct answer is option C.

Note: When the distance between two points becomes unity then the potential gradient becomes equal to potential difference between two points. Also Potential gradient is meant for a fixed value of length. When we talk about a charge at infinity then its potential gradient will become zero.