Home
Class 12
PHYSICS
A Sphere of radius R0 carries a volume c...

A Sphere of radius `R_0` carries a volume charge density proportional to the distance (x) from the origin, `rho=alphax` where `alpha` is a positive constant. (a) Calculate the total charge in the sphere of radius `R_0`. (b) The sphere is shaved off so as to reduce its radius. What should be the radius (R) of the remaining sphere so that it contains half the charge of the original sphere? (c) Find the electric field at a point inside the sphere at a distance r lt R. Give your answer for original sphere of radius `R_0` as well as for the smaller sphere of radius R that was left after shaving off the original sphere.

Text Solution

Verified by Experts

The correct Answer is:
(a). `pialphaR_(0)^(4)`
(b). `(R_(0))/((2)^(1//4))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

A sphere of radius R_(0 carries a volume charge density proportional to the distance (x) from the origin, rho=alpha x where alpha is a positive constant.The total charge in the sphere of radius R_(0) is

A sphere of radius R carries charge density p proportional to the square of the distance from the centre such that p = Cr^(2) , where C is a positive constant. At a distance R // 2 from the centre, the magnitude of the electric field is :

Knowledge Check

  • the electric field inside a sphere which carries a charge density proportional to the distance from the origin p=alpha r ( alpha is a constant) is :

    A
    `propto` `r^(3)/(4epsilon_(0))`
    B
    `propto` `r^(2)/(4epsilon_(0))`
    C
    `propto` `r^(3)/(3epsilon_(0))`
    D
    none of these

  • 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 strength 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

  • A hallow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre:

    A
    decreases as r increases for `rltR` and `rgtR`
    B
    increases as r increases for `rltR` and `rgtR`
    C
    zero as r increases for `rltR`, decreases as r increases for `rgtR`
    D
    zero as r increases for `rltR`, increases for `rgtR`

    • Similar Questions

    Explore conceptually related problems

    A spherical region of space has a distribution of charge such that the volume charge density varies with the radial distance from the centre r as rho=rho_(0)r^(3),0<=r<=R where rho_(0) is a positive constant. The total charge Q on sphere is

    Metallic sphere of radius R is charged to potential V. Then charge q is proportional to

    A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to its sphere at a distance r from its centre.

    A metal sphere of radius r is charged to certain potential V. Then the charge on the metal sphere

    A sphere of radius R has a charge density sigma . The electric intensity at a point at a distance r from its centre is

    Home
    Profile