Home
Class 12
PHYSICS
A solid spherical region, having a spher...

A solid spherical region, having a spherical cavity whose diameter R is equal to the radius of the spherical region, has a total charge Q. Find the electric field at a point P as shown in figure
.

Text Solution

Verified by Experts

The correct Answer is:
`(Q)/(28 pi epsilon_(0)) [ (8)/( x^(2)) - (1)/((x -(R)/(2))^(2))]`
Volumetric charge density of given structure is
`rho = Q/(4/3piR^3 - 4/3pi(R/2)^3) = 8/7 Q/(4/3piR^3)`

`1Q_1 = rho 4/3 piR^3 = 8/7 Q, Q_2 = rho 4/3 pi (R/2)^3 = 1/7Q`
`E_(P) = E_1-E_2 = 1/(4piepsilon_0) Q_1/x^2 - 1/(4piepsilon_0) Q_2/(x-R/2)^2`
`= Q/(28piepsilon_0) [8/x^2 - 1/(x- R/2)^2]`.
Promotional Banner

Topper's Solved these Questions

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS ENGLISH|Exercise Single Correct|40 Videos

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS ENGLISH|Exercise Multiple Correct|8 Videos

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 2.2|14 Videos

  • ELECTRIC CURRENT AND CIRCUIT

    CENGAGE PHYSICS ENGLISH|Exercise Interger|8 Videos

  • ELECTRIC POTENTIAL

    CENGAGE PHYSICS ENGLISH|Exercise DPP 3.5|15 Videos

Similar Questions

Explore conceptually related problems

Three conducting spherical shells have charges q,-2q and 3q as shown in figure. Find electric Potential at point P as shown in figure.

A spherical shell of radius R has a uniformly distributed charge ,then electric field varies as

A solid metallic sphere has a charge +3Q . Concentric with this sphere is a conducting spherical shell having charge -Q . The radius of the sphere is a and that of the spherical shell is b(bgta) What is the electric field at a distance R(a lt R lt b) from the centre

The adjacent diagram shows a charge +Q held on an insulating support S and enclosed by a hollow spherical conductor, O represent the center of the spherical conductors and P is a point such that OP=x and SP=r .The electric field at point P will be

A sphere of radius R has a uniform volume density rho . A spherical cavity of radius b, whose center lies at veca , is removed from the sphere. i. Find the electric field at any point inside the spherical cavity. ii. Find the electric field outside the cavity (a) at points inside the large sphere but outside the cavity and (b) at points outside the large sphere.

A solid sphere of radius 'R' has a cavity of radius (R)/(2) . The solid part has a uniform charge density 'rho' and cavity has no charge. Find the electric potential at point 'A'. Also find the electric field (only magnetude) at point 'C' inside the cavity

An infinitely long solid cylinder of radius R has a uniform volume charge density rho . It has a spherical cavity of radius R//2 with its centre on the axis of cylinder, as shown in the figure. The magnitude of the electric field at the point P , which is at a distance 2 R form the axis of the cylinder, is given by the expression ( 23 r R)/( 16 k e_0) . The value of k is . .

A non-conducting sphere of radius R has a spherical cavity of radius R//2 as shown. The solid part of the sphere has a uniform volume charge density rho . Find the magnitude and direction of electric field at point (a) O and (b) A.

A few spherical equipotential surfaces are shown in the figure. The electric field at any point, at a distance x from the centre, is

A Uniformly charged solid non-conducting sphere of uniform volume charge density rho and radius R is having a concentric spherical cavity of radius r. Find out electric field intensity at following points, as shown in the figure : (i) Point A (ii) Point B (iii) Point C (iv) Centre of the sphere