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A sphere of charges of radius R carries ...

A sphere of charges of radius R carries a positive charge whose volume chasrge density depends only on the distance r from the ball's centre as `rho=rho_0(1-r/R`), where` rho_0` is constant. Assume epsilon as theh permittivity of space.
The magnitude of the electric field as a functiion of the distance r outside the balll is given by

A

`E = (rho _(0) R ^(3))/(8 epsi r ^(2)`

B

`E = (rho _(0) R ^(3))/(12 epsi r ^(2))`

C

`E = (rho _(0) R ^(3))/(16 epsi r ^(2))`

D

`E = ( rho _(0) E ^(3))/(24 epsi r ^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • A sphere of charges of radius R carries a positive charge whose volume chasrge density depends only on the distance r from the ball's centre as rho=rho_0(1-r/R), where rho_0 is constant. Assume epsilon as theh permittivity of space. The magnitude of electric field as a function of the distance r inside the sphere is given by

    A
    `E=rho_0/epsilon[r/3-r^3/(4R)]`
    B
    `E=rho_0/epsilon[r/4-r^3/(3R)]`
    C
    `E=rho_0/epsilon[r/3+r^2(4R)]`
    D
    `E=rho_0/epsilon[r/4+r^2/(3R)]`

  • A sphere of charges of radius R carries a positive charge whose volume chasrge density depends only on the distance r from the ball's centre as rho=rho_0(1-r/R), where rho_0 is constant. Assume epsilon as theh permittivity of space. the maximum electric field intensity is

    A
    `E_m=(rho_0R)/(9epsilon)`
    B
    `E_m=(rho_0epsilon)/(9R)`
    C
    `E_m=(rhoR)/(3epsilon)
    D
    `E_m=(rho_0R)/(6epsilon)`

  • A sphere of charges of radius R carries a positive charge whose volume chasrge density depends only on the distance r from the ball's centre as rho=rho_0(1-r/R) , where rho_0 is constant. Assume epsilon as theh permittivity of space. The value of distance r_m at which electric field intensity is maximum is given by

    A
    `r_m=R/3`
    B
    `r_m=(3R)/2`
    C
    `r_m=(2R)/3`
    D
    `r_m=(4R)/3`