Question

The unit of linear charge density is:

• A. coulomb/metre
• B. metre/coulomb
• C. coulomb x metre
• D. none of these

Hint:

For understanding charge densities, remember the following: - Linear charge density: \( \lambda = \frac{Q}{L} \), - Surface charge density: \( \sigma = \frac{Q}{A} \), - Volume charge density: \( \rho = \frac{Q}{V} \).

Answer 1

The Correct Option is A

Linear charge density, denoted by \( \lambda \), is defined as the charge per unit length. This is a way to describe how charge is distributed along a one-dimensional object, such as a wire or a thin rod. \[ \lambda = \frac{Q}{L} \] where:

\( Q \) is the total electric charge distributed along the length of the object,
\( L \) is the total length over which the charge is distributed,
\( \lambda \) represents the amount of charge per unit length.
To understand the dimensional properties of \( \lambda \), we examine the units of its components. The SI unit of charge \( Q \) is the coulomb (C), and the SI unit of length \( L \) is the meter (m). Therefore, the unit of linear charge density is: \[ \text{Unit of } \lambda = \frac{\text{Coulomb}}{\text{Meter}} = \text{C/m} = \text{coulomb per metre}. \] This unit tells us how many coulombs of charge exist per meter of length. For example, a linear charge density of \( 5\, \text{C/m} \) means there are 5 coulombs of charge distributed uniformly along each meter of the object.