An infinitely long line charge having a uniform charge per unit length `lambda` lies at a distance d from a point O as shown in figure. Determine the total electric flux through through the surface of a sphere of radius R centered at O resulting from this line charge. Consider both cases where Rltd and Rgtd`.

Answer

`(2 lambda sqrt(R^(2) - d^(2)))/(epsilon_(0))`

Explanation

For Rltd, the flux will be zero. It is because there is no charge
line inside the sphere figure. For Rltd, the length inside the sphere is `2(sqrt(R^2-d^2))`. So the charge inside is `2lambda sqrt(R^2-d^2)`.
Thus `phi = (2lambdasqrt(R^2-d^2))/epsilon_0`