Question

IN fig, calculate the total flux of the electrostatic field through the spheres `S_(1) and S_(2)`. The wire AB shown here has a linear charge density `lambda` . Given by `lambda = kx`, where x is the distance measured along the wire from end A.

Answer 1

Charge on an element of length dx of wire AB
`dq = lambda, dx = kx dx`
Total charge on wire AB,
`q = int dq = int_(0)^(1) kx dx = k((x^(2))/(2))_(0)^(1) = (1)/(2) kl^(2)`
Total flux through `S_(1) = phi = (Q)/(in_(0))`
Total flux through `S_(2)`
`= phi_(2) = (Q+q)/(in_(0)) = (Q + (1)/(2) kl^(2))/(in_(0))`