A

Step 1: Understand the electric field due to an infinite sheet:
The electric field (E) created by a uniformly charged infinite sheet with surface charge density σ is given by:
$$E = \frac{\sigma}{2\epsilon_0}$$
where $\epsilon_0$ is the permittivity of free space. The electric field is uniform and points away from the sheet.

Step 2: Calculate the work done (W) by the external agent:
The work done by the external agent in moving a charge $q_0$ from distance $a$ to $b$ can be determined by the equation:
$$W = q_0 E (b - a)$$
Substituting the value of $E$:
$$W = q_0 \left(\frac{\sigma}{2\epsilon_0}\right) (b - a)$$

Step 3: Relating the parameters:
The formula obtained shows that the work done is directly proportional to the charge $q_0$, the surface charge density $\sigma$, and the difference in distances $(b - a)$. Thus, we can conclude:
$$W \propto q_0 \sigma (b - a)$$

Therefore, the relation between the parameters is:
$$W = kq_0 \sigma (b - a)$$
where k is a constant.

Thus, the relationship between the work done by the external agent and the given parameters is clearly established.