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A cone made of insulating material has a...

A cone made of insulating material has a total charge Q spread uniformly over its sloping surface. Calculate the work done in bringing a small test charge q from infinity to the apex of the cone. The cone has a slope length L.

Text Solution

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The correct Answer is:
B

`W=-/_\U=U_("apex")-U_oo`
`W=qV_("apex")` ………..i
`as U_prop=0`
`V_("apex") r/x=R/L `
`:. r=(R/L)x`
Surface charge density
`sigma=Q/(piRl)`
`dq=(sigma)(dA)`
`=(Q/(piRL))(2pir) (R/Xx)dx`
=`(theta/(piRL))(2pi)(R/Lx)dx`
`=((2Q)/L^2)xdx`
`Now, dV=(1/(4piepsilon_0))((dq)/x)`
`=((2Q)/(4piepsilon_0^L^(2)))dx`
`:. V=int_0^LdV=Q/(2piepsilon_0L)`
substituting in eqn i we have
`W=(Qq)/(2piepsilon_0L)`
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