An infinitely long line charge having a uniform charge per unit length $\mathrm{\lambda }$ lies a distance d, from center of imaginary sphere of radius R. Then

flux crossing the sphere is zero if d > R

If d > R, the magnitude of maximum potential difference between two points on the sphere is $\frac{\mathrm{\lambda }}{2{\mathrm{\pi \epsilon }}_0}\ln \left(\frac{\mathrm{d}+\mathrm{R}}{\mathrm{d}-\mathrm{R}}\right)$

flux crossing the sphere is $\frac{2\lambda \sqrt{R^2-d^2}}{{\epsilon }_D},\text{ if }\mathrm{d}<\mathrm{R}$

When a charge is moved along any diameter of the sphere in the plane perpendicular to the wire, work done is zero.