Question

Which of the following quantities is scalar?
(a) Dipole moment
(b) Electric force
(c) Electric field intensity
(d) Electric potential

Answer 1

Hint: Since this question includes terms only so we will apply simple definitions and use the formula to answer it. As this question asks for finding scalar quantity out of the four options so, we will find the direction in each of the terms. If in case any of the terms does not include direction in it then that will be the right answer.

Formula Used:
$\overrightarrow{F}=k\dfrac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\widehat{r}$ where k is constant of proportionality; r is the distance of separation between charges ${{q}_{1}},{{q}_{2}}$ and $\widehat{r}$ is a unit vector, $\overrightarrow{E}=\dfrac{\overrightarrow{F}}{q}$ where $\overrightarrow{F}$ is called the force and q is a charge, $V=k\dfrac{q}{r}$ where r is the distance of separation and q is a charge.

Complete step-by-step solution:
We will first understand the definition of each term.
Dipole moment: Any electric dipole is formed by two opposite charges + q and – q which are separated by a distance d (say). In an electric dipole, the direction is taken from the negative charge to the positive charge. We can measure the dipole by the product of the magnitude of charge and its distance between two equal but opposite charges. This clearly depends upon direction. So, it is a vector quantity.
Electric force: If one object interacts with another charged object then the action of attraction or repulsion between them is what we call an electric force. It is generally measured by using Coulomb’s law $\overrightarrow{F}=k\dfrac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\widehat{r}$. This also totally depends upon magnitude as well as direction because if one positive charge comes in contact to negative then it will attract it otherwise in a negative one it will repel. As it depends upon the charge which is exerting force on another so, it is a vector quantity.
Electric field intensity: It is just a calculated measurement of that force that is exerted by one object on the other object. Its formula is $\overrightarrow{E}=\dfrac{\overrightarrow{F}}{q}$ and since it is a vector quantity hence electric field intensity is also a vector quantity.
Electric potential: It is based upon the amount of force or work which is done for moving a unit charge. It is measured by $V=k\dfrac{q}{r}$. Since there is no direction involved so it is a scalar quantity.
Hence, the correct option is (d).

Note: For a term to be a vector quantity, it must include magnitude and direction both. In case of only magnitude the term will be considered as a scalar quantity. Direction plays a most important part for vector quantity. There is a property of a vector quantity which states that any scalar or a vector quantity is multiplied to a vector quantity it will result into a vector one only. The best example to explain this property is electric field intensity. Since, it includes force which is itself a vector then, it implies electric field intensity to be also a vector. One should know about the basic definitions so that we can easily answer these questions with only terms included.