Question

If gravitational field intensity is E at distance R/2 outside from then surface of thin shell of radius R the gravitational field intensity at distance R/2 from its centre is

Answer 1

Given:

Gravitational field intensity is E at distance R/2 outside from then surface of thin shell of radius R.

To find:

Gravitational field intensity at a distance R/2 from the centre.

Calculation:

Considering a spherical Gaussian surface of radius R/2 ;

Let field Intensity at that position be E2.

$\displaystyle \int \: E2 \: . \: ds = \dfrac{q}{\epsilon_{0}}$

Since the charge enclosed by the Gaussian Surface is zero ;

$\displaystyle = > \: E2 \: \int\: ds = \dfrac{q}{\epsilon_{0}}$

$\displaystyle = > \: E2 \: \int\: ds = \dfrac{0}{\epsilon_{0}}$

$\displaystyle = > \: E2 \: \int\: ds = 0$

$\boxed{ = > \: E2 \: = 0}$

So, Gravitational field intensity at a distance of R/2 is zero.

• Note that Field Intensity inside a spherical shell will always be zero because the enclosed charge is equal to zero.