In vacuum (i) find out the electric flux across an area `vec S = 10 hatj ` placed in an electric field ` vec E = 2 hati + 4 hatj + 7 hatk `, (ii) How many electric charges are to be placed at a point such that 4400 number of electric lines of forces with emerge from that point ? (iii) What will be the electric flux through any one of the faces of a cube of side 10 cm if a charge of 1 esu is placed at the centre of the cube ?

Explanation

(i) Electric flux ` phi = vecE* vec S = ( 2 hati + 4 hatj + 7 hatk ) * 10 j = 40 ` unit
(ii) In CGS system, according to Gauss' theorem, in vacuum the net electric flux linked with a closed surface is 4 ` pi` times the net charge within the surface.
` therefore 4400 = 4pi q `
or, ` q = (4400) /( 4pi ) = ( 4400 xx 7)/(4 xx 22 ) = 350 ` esu
(iii) Net electric flux ` = 4pi q = 4pi * 1 = 4pi ` esu
As a cube has 6 faces , the electric flux linked with each face of the cube ` = ( 1 ) /( 6) xx 4pi = ( 2 ) /( 3 ) pi ` esu.