Home
Class 12
PHYSICS
A sphere of radius R has a volume densit...

A sphere of radius R has a volume density of charge `rho=kr`, were r is the distance from the centre of the sphere and k is constant . The magnitude of the electric field which exists at the surface of the sphere is given by `(epsilon_(0)=` permittivity of free space)

A

`(4pikR^(4))/(3epsilon_(0))`

B

`(kR)/(3epsilon_(0))`

C

`(4pikR)/(epsilon_(0))`

D

`(kR^(2))/(4pi_(0))`

Text Solution

Verified by Experts

The correct Answer is:
d
Consider a thin spherical shell of radius x and thickness dx as shown in the figure.

Volume of the shell , `dV=4pix^(2)dx`
Let us draw a Gaussian surface od radius `r(rltR)` as shown in the figure above.
Total charge enclosed by the Gaussian surface is
`Q_("in")=int_(0)^(r)rhodV=int_(0)(r)kx4pix^(2)dx=4pikint_(0)^(r)x^(3)dx`
`=4pik[(x^(4))/(4)]_(0)^(r)=pikr^(4)`
According to Gaussa.s law
`E4pir^(2)=(Q_("in"))/(epsilon_(0))orE4pir^(2)=(pikr^(4))/(epsilon_(0))`
At the surface of the sphere , r=R
`thereforeE=(kR^(2))/(4piepsilon_(0))`
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTATICS

    MTG-WBJEE|Exercise (WB JEE Previous Years Questions ) CATEGORY 3 : One or More than One Opion correct Type|4 Videos

  • ELECTROSTATICS

    MTG-WBJEE|Exercise (WB JEE Previous Years Questions ) CATEGORY 1 : Single Option correct Type|23 Videos

  • ELECTROMAGNETIC WAVES

    MTG-WBJEE|Exercise WB JEE WORKOUT (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|10 Videos

  • GRAVITATION

    MTG-WBJEE|Exercise WB JEE Previous Years Questions (CATEGORY 1: Single Option Correct Type|7 Videos

Similar Questions

Explore conceptually related problems

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 solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression rho = Ar^2 , where A is a constant and rltR is measured from the centre of the sphere. Show that (a) the magnitude of the electric field outside (rgtR) the sphere is E = AR^5//5epsilon_0r^2 and (b) the magnitude of the electric field inside (rltR) the sphere is E = AR^3//5epsilon_0 .

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), have volume charge density rho=A/r , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the centre. What is the ratio of the magnitude of the electric field at a distance 2 R from the centre to the magnitude of the electric field at a distance of R//2 from the centre?

A Gausian sphere of radius r intercepts a line with a uniform charge density +1 as shown. The line is at a distance root 3'r/2 from the centre of the sphere. What is the electric flux associated with the Gaussian sphere?

Surface density of charge on a sphere of radius R in terms of electric intensity E at a distance in free space is (epsi_(0) = permittivity of free space)

Charge density of a sphere of radius R is rho = rho_0/r where r is distance from centre of sphere.Total charge of sphere will be

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)