In the figure shown, calculate the total flux of the electrostatic field through the sphere ` S_1 and S_2 ` The wire AB shown of length `l` has a liner charge density ` lamda ` given ` lamda = kx ` where x is the distance measured along the wire from end A.

Explanation

Total charge on wire AB =Q = ` int_o ^l lamda dx = int _o^l k x dx = (1)/(2) kl^2`
By Gauss.s theorem.
Total flux through ` S_1 = (Q)/(in_0)`
Total flux through ` S_2 = (Q+ (1)/(2) kl ^2)/(in_0)`