(a) Define electric flux . Write its S.I . Unit.
(b) A small metal sphere carrying charge `+Q` is located at the centre of a spherical cavity inside a large uncharged metallic spherical shell as shown in the figure . Use Gauss 's law to find the expressions for the electric field at point `P_(1)andP_(2)`.

(c ) Draw the pattern of electric field lines in this arrangement .

Explanation

(a) Refer to L.A.T.Q . No 3(a).
(b) Let point `P_(1)` is at distance R from the centre O.
`S_(1)` is the Gaussian surface , then according to Gauss.s theorem
`oint_(s)vecE*vecds=oint_(s)vecE*hatnds=(q)/(epsilon_(0))`
or `Eoint_(s)ds=(q)/(epsilon_(0))`
or `E=(q)/(epsilon_(0)xxoint_(s)ds)`
`=(q)/(4piepsilon_(0)R^(2)) " " [ "As"oint_(s)ds=4piR^(2)]`

Inside the shell the net charge is zero ,so the field is also zero .
(c ) The direction of electric field is shown in figure.