Home
Class 12
PHYSICS
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

Verified by Experts

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)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELECTROSTATICS

    DC PANDEY ENGLISH|Exercise Level 1 Assertion And Reason|19 Videos

  • ELECTROSTATICS

    DC PANDEY ENGLISH|Exercise Level 1 Objective|82 Videos

  • ELECTROSTATICS

    DC PANDEY ENGLISH|Exercise Exercise 24.6|2 Videos

  • ELECTROSTATIC POTENTIAL AND CAPACITORS

    DC PANDEY ENGLISH|Exercise (C) Chapter exercises|50 Videos

  • GRAVITATION

    DC PANDEY ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

A charge Q is placed at the origin. The electric potential due to this charge at a given point in space is V . The work done by an external force in bringing another charge q from infinity up to the point is

Find the electric work done in bringing a charge q from A to B in a sphere of charge Q distributed uniformly throughout its volume. .

Knowledge Check

  • Four equal charges Q are placed at the four corners of a square of each side is 'a'. Work done in removing a charge -Q from its centre to infinity is

    A
    zero
    B
    `(sqrt2q^(2))/(pi epsi_(0)a)`
    C
    `(sqrt2q)/(pi epsi_(0)a)`
    D
    `(q^(2))/(pi epsi_(0)a)`

    • Similar Questions

    Explore conceptually related problems

    (a) Use Gauss's theorem to find the electric field due to a uniformly charged infinitely Iarge plane thin sheet with surface charge density. Sigma (b) An infinitely large thin plane sheet has a uniform surface charge density + sigma . Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point , distant r, in front of the charged plane sheet.

    A rod of length L has a total charge Q distributed uniformly along its length. It is bent in the shape of a semicircle. Find the magnitude of the electric field at the centre of curvature of the semicircle.

    A spherical shell made of plastic, contains a charge Q distributed uniformly over its surface. What is the electric field inside the shell? If the shell is hammered to deshape it without altering the charge. Will the field inside be changed? What happend if the shell is made of a metal?

    A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of -2xx10^(-9) from a point P(0, 0, 3cm) to a point Q (0, 4cm, 0) via a point R(0, 6cm, 9cm).

    A cjircular wire-loop of radius a carries a total charge Q distributed uniformly over its length . A small length dL of the wire is cut off. Find the electric field at the centre due to remaining wire.

    A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0lerltoo , where r is the distance from the centre of the shell?

    A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0lerltoo , where r is the distance from the centre of the shell?

    Home
    Profile