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A sphere of radius R contains charge den...

A sphere of radius R contains charge density `rho(r )=A (R-r )`, for `0 lt r lt R`. The total electric charge inside the sphere is Q.
The value of A in terms of Q and R is

A

`(2Q^(2))/(piR^(4))`

B

`(3Q)/(pi R^(4))`

C

`(3Q^(2))/(pi R^(3))`

D

`(3Q)/(pi R)`

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Knowledge Check

  • Consider a sphere of radius R with unform charged density and total charge Q. The electrostatic potential distribution inside the sphere is given by phi (r ) =(Q )/( 4 pi epsi_0 R) (a + b ( r//R)^c ) Note that the zero of potential is at infinity. The values of (a, b, c) are :-

    A
    `(1/2, -3/2 ,1)`
    B
    `(3/2, -1/2 ,2)`
    C
    `(1/2, 1/2 ,1)`
    D
    `(1/2, -1/2 ,2)`

  • An insulating solid sphere of radius R has a uniformaly positive charge density rho . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement-1: Wgen a charge 'q' is taken from the centre to the surface of the sphere, its potential energy charges by (qrho)/(3 in_(0)) Statement-2 : The electric field at a distance r (r lt R) from the centre of the the sphere is (rho r)/(3in_(0))

    A
    Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1
    B
    Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
    C
    Statement-1 is true, Statement-2 is false
    D
    Statement-1 is false, Statement-2 is true

  • A solid sphere of radius R_(1) and volume charge density rho = (rho_(0))/(r ) is enclosed by a hollow sphere of radius R_(2) with negative surface charge density sigma , such that the total charge in the system is zero . rho_(0) is positive constant and r is the distance from the centre of the sphere . The ratio R_(2)//R_(1) is

    A
    `(sigma)/(rho_(0))`
    B
    `sqrt((2 sigma)/(rho_(0)))`
    C
    `sqrt((rho_(0))/(2 sigma))`
    D
    `(rho_(0))/(sigma)`

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