Charge 􀀓 is applied to a circular disk of ebonite of radius 􀀔 by rubbing it while it is rotating. In
this way the surface charge density becomes proportional to the radial distance from the
center. Show that the electric field strength on the axis of the disk at an axial distance ℎ from
the center is 􀀖􀀗􀀘
􀀙􀀌􀀚􀀛􀀜􀀝 􀀞􀀟􀀠 􀀜􀀡√􀀜􀀣􀀡􀀘􀀣
􀀘 − 􀀥
√􀀜􀀣􀀡􀀘􀀣􀀦 􀀧􀀨.

Question

Rasanjana Weerarathne · Answer

Charge Q is applied to a circular disk of ebonite of radius a by rubbing it while it is rotating. in this way, the surface charge density becomes proportional to the radial distance from the center. Show that the electric field strength on the axis of the disk at an axial distance h from the center is E = 3 Q h 4 π ϵ 0 a 3 [ ln a + a 2 + h 2 − − − − − − − √ h − 1 a 2 + h 2 − − − − − − − √ ] a n

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