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
.

A

`(Q)/(18 pi epsilon_(0)) [ (4)/( x^(2)) - (1)/((x -(R)/(2))^(2))]`

B

`(Q)/(28 pi epsilon_(0)) [ (8)/( x^(2)) - (1)/((x -(R)/(2))^(2))]`

C

`(Q)/(28 pi epsilon_(0)) [ (8)/( x^(2)) - (1)/((x -R)^(2))]`

D

`(Q)/(18 pi epsilon_(0)) [ (4)/( x^(2)) - (1)/((x -R)^(2))]`

Text Solution

Verified by Experts

The correct Answer is:
B
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|Exercise Single Correct|40 Videos

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS|Exercise Multiple Correct|8 Videos

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS|Exercise Exercise 2.2|14 Videos

  • ELECTRIC CURRENT AND CIRCUIT

    CENGAGE PHYSICS|Exercise Interger|8 Videos

  • ELECTRIC POTENTIAL

    CENGAGE PHYSICS|Exercise DPP 3.5|14 Videos

Similar Questions

Explore conceptually related problems

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

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 charge +q units. The electric field due to the shell at a point

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

Given below are two statements : Statement I : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere. Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (lt R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero. In the light of the above statements, choose the correct answer from the options given below :

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.

Knowledge Check

  • 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
    `kq(1/2r-1/r)`
    B
    `kq(1/R-1/r)`
    C
    `kq(1/(2R)-1/r)`
    D
    `(kq)/r-(k(2q))/r+(k_(3q))/(R)`
    Here `=kq(1/R-1/r)`

  • A spherical shell of radius R has a charge +q units. The electric field due to the shell at a point

    A
    inside is zero and varies as `r^(-1)` outside it
    B
    inside is constant and varies as `r^(-2)`
    C
    inside is zero and varies as `r^(-2)` outside it
    D
    inside is constant and varies as `r^(-1)` outside it

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

    A
    inside is zero and varies as `x^(-1)` outside it
    B
    inside is non zero constant and varies as `x^(2)` outside it
    C
    inside is zero and varies as `x^(-2)` outside it
    D
    inside is constant and varies as `x^(-1)` outside it