Question

Write the name of a physical quantity whose unit is $J{{C}^{-1}}$. State whether this quantity is vector or scalar.

Answer 1

Hint: We know that $J$ is the unit of energy and $C$ is the unit of charge. Also do we know that a vector quantity has both direction and magnitude whereas a scalar quantity has only magnitude. The physical quantity to be named can be identified using the relation between energy and charge.

Complete answer:
We are supposed to find a physical quantity which is related to energy as well as charge. We know that energy is a measure of work. Therefore, we can relate the physical quantity to a charge as well as the work done. This physical quantity is nothing but electrostatic potential. Electrostatic potential at any point in a region of electric field is defined as the minimum work done to carry a unit positive charge from infinity to that point, without acceleration. Mathematically, it is represented as:
${{V}_{P}}=\dfrac{{{W}_{\infty P}}}{q}$
where
${{V}_{P}}$ is the electrostatic potential at a point $P$ in a region of electric field
${{W}_{\infty P}}$ is the word done to carry a unit positive charge $q$ from infinity to the point $P$, without acceleration
The SI unit of electrostatic potential is $volt(V)$. Electrostatic potential at a point is said to be $1V$, when $1J$ of work is done in moving $1C$ of charge from infinity to that point against the electrostatic force of the field without acceleration. Clearly,
$1V=\dfrac{1J}{1C}=1J{{C}^{-1}}$
It is important to note that the work done in bringing a unit positive charge from infinity to a point against electrostatic force without acceleration is independent of the path. This suggests that the charge can be brought along any path between infinity and that particular point. The direction of movement of charge is not important. This suggests that electrostatic potential is a scalar quantity.

Additional information:
A scalar quantity has magnitude but no direction. It is only dependent on the initial point and the final point. Some examples of scalar quantities are mass, speed, area, volume and temperature. A vector quantity has both magnitude as well as direction. It is dependent on the path between the initial point and the final point. Some examples of vector quantities are acceleration, displacement, force and electric field intensity.

Note:
Electrostatic potentials at two different points in a region of electric field can be used to determine the electrostatic potential difference between the given points. Electrostatic potential difference between two points $A$ and $B$ is defined as the amount of work done in carrying a unit positive charge from $A$ to $B$ without acceleration, against the electrostatic force and along any path between the given points. Mathematically, electrostatic potential difference is expressed as:
${{V}_{AB}}=\dfrac{{{W}_{AB}}}{q}={{V}_{A}}-{{V}_{B}}$
where
${{V}_{AB}}$ is the potential difference between $A$ and $B$
${{W}_{AB}}$ is the word done to carry a unit positive charge $q$ from $A$ to $B$ , without acceleration
${{V}_{A}}$ is the electrostatic potential at point $A$
${{V}_{B}}$ is the electrostatic potential at point $B$
Clearly, electrostatic potential difference is the difference in electrostatic potentials at the two given points.