Introduction:
In this scenario, we have a series of plates with surface area A on one side and a separation distance d between consecutive plates. The plates are connected to a battery with an electromotive force (emf) E. We need to determine the magnitude of charge transferred through the battery.

Understanding the Situation:
To understand the situation better, let's break it down into smaller components:

1. Plate Configuration: The plates are arranged in a series, meaning that the positive terminal of the battery is connected to one plate and the negative terminal is connected to the adjacent plate. This creates a uniform electric field between the plates.

2. Electric Field: The electric field between the plates is given by the equation E = V/d, where E is the electric field strength, V is the potential difference between the plates, and d is the separation distance.

3. Charge Transfer: When a potential difference is applied across the plates, charges (electrons in this case) start to move from the negative plate towards the positive plate. This movement of charges is known as charge transfer.

Determining the Charge Transferred:
To determine the magnitude of charge transferred through the battery, we can use the equation Q = CV, where Q is the charge transferred, C is the capacitance, and V is the potential difference.

1. Capacitance: The capacitance of the plate configuration can be calculated using the formula C = εA/d, where C is the capacitance, ε is the permittivity of the medium between the plates, A is the surface area of the plates, and d is the separation distance.

2. Potential Difference: The potential difference between the plates can be obtained from the emf of the battery, which is given by V = Ed, where V is the potential difference, E is the emf, and d is the separation distance.

3. Charge Transfer: Substituting the values of capacitance and potential difference into the equation Q = CV, we get Q = (εA/d) * (Ed), which simplifies to Q = εAE.

Therefore, the magnitude of charge transferred through the battery is given by Q = εAE.

Conclusion:
In this scenario, the magnitude of charge transferred through the battery is given by the equation Q = εAE, where Q is the charge transferred, ε is the permittivity of the medium between the plates, A is the surface area of the plates, and E is the emf of the battery. This equation can be derived by considering the capacitance of the plate configuration and the potential difference between the plates.