2.2 - Charge Density When enough charge has built up on a given surface, the res

Question

2.2 - Charge Density

When enough charge has built up on a given surface, the resulting strength of electric field can ionize the air surrounding the surface, creating a way for charge to escape the surface and transfer to molecules in the air. There is therefore a maximum amount of charge that you can effectively keep on the surface of a given object (in air) without this happening. You may have seen this before in the form of sparks when you receive an electric shock. It turns out that the maximum charge density a surface can maintain before ionization occurs is about 510 5 C/m2. If the charge is evenly spread out, what is the maximum charge that can be carried on the surface of a sphere with a radius of .25 cm ?

Explanation / Answer

Maximum Surface Charge density, given=5*10^(5) C/m2

Maximun Surface charge density= maximum charge (Qmax)* Surface area of the body

here, Surface area of body=4*3.14*r2 =4*3.14*(0.25*10^(-2))^2

Surface area = 7.85*10^(-5) m2

Qmax=Max surface charge density/surface area = 5*10^(5)/7.85*10^(-5)

Qmax =6.37*10^(9) Coulombs

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