Question

The SI unit of surface charge density is
A. $\text{C}\cdot {{m}^{-1}}$
B. $\text{C}\cdot {{m}^{-2}}$
C. $\text{C}\cdot {{m}^{-3}}$
D. $\text{C}$

Answer 1

Hint: Determine the expression for surface charge density. Substitute the SI units of all the quantities used in the formula. Obtain the SI units of surface charge density using units of other quantities involved.
Formula used:
$\sigma =\dfrac{q}{A}$

Complete answer:
Surface charge density is a quantity which gives the amount of charge accumulated on a surface per unit area. Thus, surface charge density for any surface can be defined as charge per unit area. It can be mathematically written as,
$\sigma =\dfrac{q}{A}$
Here, $\sigma $ represents surface charge density, $q$ represents charge and $A$ represents area.
Now, we know that SI unit of charge is Coulomb which is denoted by $\text{C}$. The SI units of length is metre ($m$). Area is defined as a product of two length measurements. Thus, the SI unit of area will be ${{m}^{2}}$.
Now, use the SI units of charge and area to determine the SI units of surface charge density. It can be seen as,
$\begin{align}
  & \sigma =\dfrac{q}{A} \\
 & =\dfrac{\text{C}}{{{m}^{2}}} \\
 & =\text{C}\cdot {{m}^{-2}}
\end{align}$

Thus, the correct option is (B).

Note:
Take care of the SI units of the quantities involved in the expression for surface charge density. Area is defined as a product of length and breadth. Since both length and breadth are linear measurements, the SI unit of area will be ${{m}^{2}}$.