Q. Acone made of insulatong material has a total charge Q spread uniformlyover its sloping surface. Calculate the work done in bringing a smalltest chrge q from infiniy to the apex of the cone. The cone has a slopelength 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

Approved