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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; σ=qA,

The SI unit of surface charge density is Cm–2.

Example 1

1. A large plane sheet has an area 50 cm2 and has a charge of 3mC uniformly distributed over it. Find the surface charge density.

Solution:

q = 3 mC = 3 × 10–3 C, A = 50 cm2 = 5 ×10–3 m2, σ = ?

σ=qA=3×10−−35×10−−3=0.6Cm−−2

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 cm2 = 15 × 10–4 m2

Charge density; σ= 2.5 ×10–2 Cm–2

Charge enclosed; q=σA=2.5×10−−2×15×10−−4=37.5×10−−6C=37.5μC

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)