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.

Question

vikas askiitian expert · Answer

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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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.

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.

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