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What is potential at a distance r (lt R...

What is potential at a distance `r (lt R)` in a dielectric sphere of uniform charge density `rho`, radius R and dielectric constant `epsilon_(r)`.

Text Solution

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`V_(A)=V_(B)+(W_(B rarr A))/(q)`
`V=(Q)/(4pi in_(0)R)+underset(R)overset(r)int (rho r)/(3 in_(0)in_(r))(-dr)=(Q)/(4 pi in_(0)R)+(rho (R^(2)-r^(2)))/(3 in_(0) in_(r))`
`V_("outside")=(KQ)/(r)`
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Knowledge Check

  • The potential at a distance R//2 from the centre of a conducting sphere of radius R will be

    A
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    B
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    C
    `(Q)/(4pi epsilon_(0)R)`
    D
    `(Q)/(2pi epsilon_(0)R)`

  • A charge Q is uniformly distributed in a dielectric sphere of radius R (having dielectric constant unity). This dielectric sphere is enclosed by a concentric spherical shell of radius 2R and having uniformly distributed charge 2Q. Which of the following graph correctly represents variation of electric field with distance r from the common centre?

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  • Potential difference beween centre and surface of the sphere of radius R and uniorm volume charge density rho within it will be

    A
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    B
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