Final answer:
To calculate the work done by moving a charge near a sheet with surface charge density, one needs to determine the electric field created by the sheet and use the formula W = qEd, considering the direction of movement relative to the electric field.
Step-by-step explanation:
To calculate the work done in moving a charge in the presence of a surface charge with a given density, we first need to know the electric field created by the sheet. A sheet of charge with a constant surface charge density σ creates an electric field that is perpendicular to its surface and has a magnitude given by E = σ / (2ε0). The work done in moving a charge q from point A to point B in an electric field E is calculated using the formula W = qEd, where d is the displacement in the direction of the electric field.
In this case, since the sheet of charge lies on the x = 0 plane and has a density (σ) equals space 40 nC/m², we can find the electric field generated by the sheet. If a charge were to move parallel to the sheet, the work done would be zero, since the displacement is perpendicular to the direction of the electric field. If the charge moves perpendicular to the sheet (along the x-axis), we would use the above formula by substituting the known values for q, E, and d to find the work done.