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