Question

Consider a thin spherical shell of radius R consisting of uniform surface charge density `sigma`. The electric field at a point of distance x from its centre and outside the shell is
A. inversely proportional to `sigma`
B. directly proportional to `x^(2)`
C. directlr proportional to R
D. inversely proportional to `x^(2)`

Answer 1

Correct Answer - D
For a thin uniformly charged spherical shell,
the field points outside the shell at a distance x from the centre is
`E=1/(4piepsilon_(0))Q/x^(2)`
If the radius of the sphere is R. `Q=sigma4piR^(2)`
`therefore" " E=1/(4piepsilon_(0))(sigma4piR^(2))/x^(2)=(sigmaR^(2))/(epsilon_(0)x^(2))`
This is inversely proportional to square of the distance from the centre. It is as if the whole charge is concentrated at the centre.