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Q. A cone made of insulatong material has a total charge Q spread uniformly over its sloping surface. Calculate the work done in bringing a small test chrge q from infiniy to the apex of the cone. The cone has a slope length L.
R/H = tan@ consider an elemental ring of radius r at a diistance x from apex ... charge on this this ring is dQ = (charge dencity * area of ring) =(Q/2piRH)(2pir dx) =Qr dx/RH .............1 potential due of this part at apex is dV = kdQ/x = (kQr /RH) (dx/x) ...................2 now againg using tan@ = r/x = R/H using above result , now eq 2 becomes dV = kQ dx/H2 integrating this , V = kQ/H now , H = Lcos@ so V = kQ/Lcos@ ...................4 this is the required result
R/H = tan@
consider an elemental ring of radius r at a diistance x from apex ...
charge on this this ring is dQ = (charge dencity * area of ring)
=(Q/2piRH)(2pir dx)
=Qr dx/RH .............1
potential due of this part at apex is
dV = kdQ/x = (kQr /RH) (dx/x) ...................2
now againg using tan@ = r/x = R/H
using above result , now eq 2 becomes
dV = kQ dx/H2
integrating this ,
V = kQ/H
now , H = Lcos@ so
V = kQ/Lcos@ ...................4
this is the required result
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