Home
Class 12
PHYSICS
Let there be a spherically symmetric cha...

Let there be a spherically symmetric charge distribution with charge density varying as `rho(r)=rho(5/4-r/R)` upto `r=R`, and `rho(r)=0` for `rgtR`, where r is the distance from the origin. The electric field at a distance r(rltR) from the origin is given by

A

` (4 pi rho_0r)/(3varepsilon_0) (5/3 -r/R)`

B

` (4 pi rho_0r)/(3varepsilon_0) (5/3 -r/R)`

C

` (4 pi rho_0r)/(3varepsilon_0) (5/4 -r/R)`

D

` (4 pi rho_0r)/(3varepsilon_0) (5/4 -r/R)`

Text Solution

Verified by Experts

The correct Answer is:
B
Consider a sherical shell of radius `x` and thickness dx.
Charge on it dq
`dq = prop xx 4 pi x^2 . Dx`
` dq = prop_0 (5/4 - x/R) xx 4 pi x^2 dx`
`q = 4 pi prop _0 int_0^r ((5 x^2)/4 - x^3/R) dx`
`q = 4 prop_0 ( (5r^3)/( 3 xx 4) - r^2/(4R))`
`E = (kq)/r^2 = 1/( 4 pir^2) xx 4 pi prop_0 ((5r^3)/( 3xx4) - r^4/(4R))`
` E = ( prop_0r)/(4 prop_0) (5 /3 - r/R)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let there be a spherical symmetric charge density varying as p(r )=p_(0)(r )/(R ) upto r = R and rho(r )=0 for r gt R , where r is the distance from the origin. The electric field at on a distance r(r lt R) from the origin is given by -

[" Consider a spherical symmetric "],[" charge distribution with charge "],[" density varying as "],[[rho={[rho_(0)(1-(r)/(R)),r R]]

Consider a spherical symmetric charge distribution with charge density varying as rho={[rho_(0)(1-(r)/(R)),r R]} The electric field at r , r le R will be

A point charge q is placed at the origin . How does the electric field due to the charge very with distance r from the origin ?

The mass density of a spherical body is given by rho(r)=k/r for r le R and rho (r)=0 for r > R , where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :

In a spherical distribution , the charge density varies as rho(r)=A//r " for " a lt r lt b (as shown) where A is constant . A point charge Q lies at the centre of the sphere at r = 0 . The electric filed in the region altrltb has a constant magnitude for

For spherically symmetrical charge distribution, electric field at a distance r from the centre of sphere is vec(E)=kr^(7) vec(r) , where k is a constant. What will be the volume charge density at a distance r from the centre of sphere?

For a spherically symmetrical charge distribution electric field at a distance r from the centre of sphere is vec(E)=kr^(2)hat(r) where k is a constant what will be the volume charge density at a distance r from the centre of sphere?