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Problem Description :
An arrangement of several ‘charged’ discs is done such that all of them subtend the same solid angle Ω at point A. This arrangement is shown in the figure below. The discs are charged positively and negatively alternately (starting with positive first). Magnitude of surface charge density of charged discs is ‘σo’ .
‘x’ is the distance from point A representing the position (used to actually point out the location of discs). It is given as :
x = nxo ….(I)
where, n belongs to natural numbers
xo is a constant
Also, similarly the surface charge density (σ) can be represented as a function (for clarity) as :
σ = (-1)n + 1 σo .…(II)
Question Parts :
(a) when x = xo , the radius of the disc is 2Ro . Find the function of radius of the disc (R) as a function of x using constants xo , Ro
(b) The radius of the last disc (for greatest n) in this arrangement is 42 Ro . Find the Electric field at point A due to the whole system.
(c) All these discs are merged together giving rise to a single disc of ‘some’ pattern. A negatively charged black coloured ink is made to be put over this merged disc. Draw down the final presentation of the disc. (Optional)
Hint : ‘n’ represents the disc number in the arrangement shown in the figure
Enjoy Solving !!
Solution has been uploaded – SOLUTION
