Surface charge density is a measure of how much electric charge is accumulated over a surface. It is calculated as the charge per unit surface area.
If q is the charge and A is the area of the surface, then the surface charge density is given by; \[\sigma = \frac{q}{A}\], The SI unit of surface charge density is Cm^{–2}.
Example 1 1. A large plane sheet has an area 50 cm^{2} and has a charge of 3mC uniformly distributed over it. Find the surface charge density. Solution:
2. A cuboidal box penetrates a huge plane sheet of charge with uniform surface charge density 2.5×10^{–2} Cm^{–2} such that its smallest surfaces are parallel to the sheet of charge. If the dimensions of the box are 10 cm × 5 cm × 3 cm, then find the charge enclosed by the box. Solution: Charge enclosed by the box = charge on the portion of the sheet enclosed by the box. The area of the sheet enclosed; A = area of the smallest surface of the box = 5 cm × 3 cm = 15 cm^{2} = 15 × 10^{–4} m^{2} Charge density; \[\sigma \]= 2.5 ×10^{–2} Cm^{–2} Charge enclosed;\[q = \sigma A = 2.5 \times {10^{--2}} \times 15 \times {10^{--4}} = 37.5 \times {10^{--6}}C = 37.5\,\mu C\]
Practice question: The same charge is given to four thin plane laminas of different shapes; an equilateral triangle, a square, a regular hexagon and a circular one. All of these have the same perimeter. Then the lamina with the maximum surface charge density has the shape as that of : (a) an equilateral triangle (b) a square (c) a regular hexagon (d) a circle Ans (a)