Question

Define linear charge density. Mention its SI unit.

Answer 1

Hint: The concept of linear charge density is used when we are considering a situation where charges are distributed on a straight line or when the charges are distributed on a line. It is also called line charge density.

Formula used: In this solution we will be using the following formulae;
$\lambda = \dfrac{q}{l} $ where $ \lambda $ is the linear charge density, $ q $ is the charge and $ l $ is length.

Complete answer:
The linear charge density as any density is a measure of how much of a particular quantity is within a particular dimension of space (length, Area or Volume). Mass density for example is the quantity mass per unit volume (a spatial dimension).
Specifically, the linear charge density can be fundamentally defined as the quantity of charge on a line per unit length of that line. From this, we can derive the unit. Charge per unit length would be given as
$\lambda = \dfrac{q}{l} $ where $ \lambda $ is the symbol often used for the linear charge density, $ q $ is the charge and $ l $ is length. Thus the unit is given as the unit of charge over the unit of length as in $ \dfrac{C}{m} = C{m^{ - 1}} $ or $ C/m $ .
It is essentially used when the charges are distributed on a charge or when the cross-sectional dimensions are negligible relative to the length of the line considered.
It is a measure of how much charge is in a unit length, that is to say it is a measure of how congested or how spread out charges are on a particular line. The higher the value, the higher the closeness of the charges together. For example, to say that the value of the linear charge density of a line charge distribution (charges distributed on a line) is X C/m is to say that there are X Coulomb of charge in every meter interval of length in that distribution.
Hence, as demonstrated from definition, the SI unit of linear charge density is C/m.

Note:
In practice, the linear charge density is employed during continuous charge distribution analysis. This is a situation where charges, though discrete, are so cramped together that they cannot be analysed easily as such, thus for most applications are considered continuous.