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The intensity of an electric field depen...

The intensity of an electric field depends only on the co-ordinates x, y and z as follows:
`vecE=a((xhati+yhatj+zhatk))/((x^2+y^2+z^2)^(3//2))`unit.
The electrostatic energy stored between two imaginary concentric spherical shells of radii R and 2R with centre at origin is

A

`(4piepsilon_0a^2)/R`

B

`(2piepsilon_0a^2)/R`

C

`(piepsilon_0a^2)/R`

D

`(piepsilon_0a^2)/(2R)`

Text Solution

Verified by Experts

The correct Answer is:
C
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The intensity of an electric field depends only on the coordinates x and y as follows, E = (a(xhati +y hatj))/(x^(2)+y^(2)) where, a is constant and hati and hatj are the unit vectors of the x and y axes. Find the charges within a sphere of radius R with the centre at the origin.

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Knowledge Check

  • The capacitance of two concentric spherical shells of radii R_(1) and R_(2) (R_(2) gt R_(1)) is

    A
    `4pi epsi_(0)R_(2)`
    B
    `4pi epsi_(0) ((R_(2)-R_(1)))/(R_(1)R_(2))`
    C
    `4pi epsi_(0) (R_(1)R_(2))/((R_(2)-R_(1)))`
    D
    `4pi epsi_(0) R^(1)`

  • The electric field at a distance (3R)/2 from the centre of a charged conducting spherical shell of radiu R is E. The electric field at a distance R/2 from the centre of the sphere is:

    A
    zero
    B
    E
    C
    `E/2`
    D
    `E/3`

  • The electric field at a distance (3R)/2 from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance R/2 from the centre of the sphere is :

    A
    `E`
    B
    `3E/2`
    C
    `E/2`
    D
    Zero

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