Question

Define the following term.
Linear charge density.

Answer 1

Hint
The amount of electrical charge per unit length in the case of linear charge distribution at any point is determined in terms of linear charge density. It is denoted by $\lambda$. It’s unit is ${\displaystyle \frac{C}{m}}$.

Complete step by step answer
Consider a continuous distribution of charge except for the configurations of charge that only includes the discrete value of charges. For a linear distribution of charge over a wire such that ‘$\mathrm{d}\mathrm{l}$’ represents a small line element of wire on the microscopic level. If ‘dq’ is the amount of charge enclosed in the line element, then the rate of the amount of charge per unit length for the line element is represented in terms of linear charge density by the relation,
$\lambda ={\displaystyle \frac{\mathrm{d}\mathrm{q}}{\mathrm{d}\mathrm{l}}}$
The SI unit of linear charge density is Coulomb per metre.

Additional Information
Similarly, the amount of electric charge can be determined in the cases of surface and volume charge distributions in terms of surface charge density and volume charge density respectively.
For a surface distribution of charge over a conductor such that ‘$\mathrm{d}\mathrm{s}$’ represents small area element of a conductor and ‘dq’ is the amount of charge enclosed in that area, surface charge density is expressed as,
$\sigma ={\displaystyle \frac{\mathrm{d}\mathrm{q}}{\mathrm{d}\mathrm{s}}}$
The SI unit of surface charge density is Coulomb per metre square.
For a volume distribution of charge over a conductor such that ‘$\mathrm{d}\mathrm{v}$’ represents small volume element of a conductor and ‘dq’ is the amount of charge enclosed in that volume, volume charge density is expressed as,
$\sigma ={\displaystyle \frac{\mathrm{d}\mathrm{q}}{\mathrm{d}\mathrm{v}}}$
The SI unit of linear charge density is Coulomb per metre cube.

Note
The small line element of the wire is considered on the macroscopic level that could include a great number of microscopic charge elements such as electrons. The charge distribution over the microscopic level is not considered because that represents a discontinuous distribution of charge.