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A solid sphere of radius R has a charge ...

A solid sphere of radius R has a charge Q distributed in its volume with a charge density `rho = kr^(a)` where .k. and .a. are constants and r is the distance from its centre. If the electric field at `r = (R )/(2)` is `(1)/(8)` times that at r = R, find the value of a.

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2
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Knowledge Check

  • A conducting sphere of radius r has a charge. Then

    A
    The charge is uniformly distributed over its surface, if there is an external electric field.
    B
    Distribution of charge over its surface will be non uniform if no external electric field exist in space.
    C
    Electric field strenght inside the sphere will be equal to zero only when no external electric field exists
    D
    Potential at every point of the sphere must be same

  • The diagram shows a uniformly charged bemisphere of radius R. It has volume charge density rho . If the electric field at a point 2R distance below its centre ?

    A
    `(rhoR)/(6epsilon_(0))+E`
    B
    `(rhoR)/(12epsilon_(0))-E`
    C
    `(-rhoR)/(6epsilon_(0))+E`
    D
    `(rhoR)/(24epsilon_(0))+E`

  • The density inside a solid sphere of radius r varies as rho (r ) = rho_(0) ((r )/(R ))^(beta), " where " rho_(0) and beta are constants and r is the distance from the centre. Let E_(1) and E_(2) be gravitational fields due to sphere at distance (R )/(2) and 2R from the centre of sphere. If (E_(2))/(E_(1)) =4 , teh value of beta is

    A
    2
    B
    2.5
    C
    3
    D
    4