Home
Class 12
PHYSICS
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 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`

Text Solution

Verified by Experts

The correct Answer is:
C
For outside the ball, electric field will continuously decreases
Hence, it will be maximum somewhere inside the ball. For maximum value,
`(dE)/(dr)=0 therefore d/(dr) [p_0/e(r/3-r^2/(4R)]=0` , Solving we get `r=(2R)/3`
Promotional Banner

Similar Questions

Explore conceptually related problems

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 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 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 ball of radius R carries a positive charge whose volume charge depends only on the distance r from the ball's centre as: rho=rho_(0)(1-(r)/(R)) Where r_(0) is a constant. Take epsilon to be permittivit of the ball. Calculate the maximum electric field intensity at a point (inside or outside the ball) due to such a charge distribution.

A ball of radius R carries a positive charge whose volume density depends according only on a separation r from the ball's centre as rho = rho_(0) (1 - r//R) , where rho_(0) is a constant. Asumming the permittivites of the ball and the enviroment to be equal to unity find : (a) the magnitude of the electric field strength as a function of the distance r both inside and outside the ball : (b) the maximum intensity E_(max) and the corresponding distance r _(m) .

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

A ball of radius R carries a positive charges whose volume density at a point is given as rho=rho_(0)(1-r//R) , Where rho_(0) is a constant and r is the distance of the point from the center. Assume the permittivies of the ball and the enviroment to be equal to unity. (a) Find the magnitude of the electric field strength as a function of hte distance r both inside and outside the ball. (b) Find the maximum intensity E_("max") and the corresponding distance r_(m) .

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

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 :