Home
Class 11
PHYSICS
A solid non conducting sphere of radius ...

A solid non conducting sphere of radius R has a non-uniform charge distribution of volume charge density, `rho=rho_(0)r/R`, where `rho_(0)` is a constant and r is the distance from the centre of the sphere. Show that : (i) the total charge on the sphere is `Q=pirho_(0)R^(3)` (ii) the electric field inside the sphere has a magnitude given by, `E=(KQr^(2))/R^(4)`

Text Solution

Verified by Experts

The correct Answer is:
`0, (2Klambda)/r, 0`
(i) `q=int dq=underset(0)overset(R)(int) rho_(0) r/Rxx4pi r^r=(rho_(0)x4pi R^(4))/R=pi rho_(0)R^(3)`
(ii) `E=(KQ')/r^(2)=K/r^(2)xx(rho_(0)pir^(4))/R=(KQr^(2))/R^(4)` where
`Q'=underset(0)overset(tau)(int)rho_(0)x/Rxx4pix^(2)dx=rho_(0)/(4R)xx4pixxr^(4)=(rho_(0)pi r^(4))/R`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN|Exercise Exercise-05(A)|35 Videos

  • MISCELLANEOUS

    ALLEN|Exercise Exercise-05(B)|19 Videos

  • MISCELLANEOUS

    ALLEN|Exercise Exersice-04[A]|34 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN|Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN|Exercise EXERCISE-IV|8 Videos

Similar Questions

Explore conceptually related problems

A solid sphere of radius R has a mass distributed in its volume of mass density rho=rho_(0) r, where rho_(0) is constant and r is distance from centre. Then moment of inertia about its diameter is

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.

Knowledge Check

  • 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 , the value of a is

    A
    3
    B
    5
    C
    2
    D
    7

  • A solid sphere of radius R has a volume charge density rho=rho_(0) r^(2) (where rho_(0) is a constant ans r is the distance from centre). At a distance x from its centre (for x lt R ), the electric field is directly proportional to :

    A
    `1//x^(2)`
    B
    `1//x`
    C
    `x^(3)`
    D
    `x^(2)`

  • An insulating solid sphere of the radius R is charged in a non - uniform manner such that the volume charge density rho=(A)/(r ) , where A is a positive constant and r is the distance from the centre. The potential difference between the centre and surface of the sphere is

    A
    `(AR)/(8epsilon_(0))`
    B
    `(AR)/(4epsilon_(0))`
    C
    `(AR)/(epsilon_(0))`
    D
    `(AR)/(2epsilon_(0))`

    • Similar Questions

    Explore conceptually related problems

    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 r=R , find the value of a.

    A system consists of a uniformly charged sphere of radius R and a surrounding by a medium with volume charge density rho =a/r , where alpha is a positive constant and r is the distance from the centre of the sphere. If NalphaR^(2) is the charge on the sphere when the electric field intensity outside the sphere is independent of r. What is the value of N ?

    A system consists of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density rho=alpha/r , where alpha is a positive constant and r is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of R.

    A system consits of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density rho=alpha/r , where alpha is a positive constant and r is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of R.

    An insulating solid sphere of the radius R is charged in a non - uniform manner such that the value charge density rho=(A)/(r ) , where A is a positive constant and r is distance from the centre. The potential difference between the centre and surface of the sphere is

    Home
    Profile