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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]`.
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Knowledge Check

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