If a battery (cell) was elongated, will it have higher voltage?

Question

Voltage is the potential difference between the terminals of the battery,and this potential difference is created by the work that the chemicals inside the battery had done.

Also, work done is determined by the force between the charges and the distance through which they are separated. That is, work done by the battery is given by the Force (between charges of both terminals) multiplied (or integrated) with the distance of separation.

Now, if I take a 1.5 volt cell (with its electrons concentrated at the negative terminal) and pull it and elongate it (supposing it still works) and move the electrons away from the positive terminal, with my external force, then will my work get stored as potential energy and hence increase the voltage of the cell?

Answer 1

The general charge storage configuration (of rechargeable batteries) is one of sheets with an electrolyte in between.

Depending on what outside form you want the manufacturer creates sheets with some length-width ratio, and these sheets are either rolled up in a cilinder or folded in some way.

Obviously, to produce a battery with an outside cilindrical form the battery manufacturer will roll the sheets into cilinders

To fit a battery with some rectangular shape the sheet will be folded in some way.

The same volume can be accommodated with a range of ratios of width and height. In the case of batteries with cilindrical outside form: it is for purpose of facilitating mass production that the industry has settled on a particular set of width-height ratios.

But in principle the width-height ratio is not a factor in how much voltage the battery will present.

The amount of voltage arises from the battery chemistry that is used.

The capacity of the battery arises from the total area of sheet that is in the battery. The larger the volume of the battery unit, the larger the area of sheet that fits into that volume.

(However, making a battery unit too voluminous creates a problem: when charging and when discharging some heat is produced. In a battery unit that is too large the risk of dangerously high temperature is too high.)

Going back to width-height ratio:
Changing the width-height ratio, without changing the volume, will not make a difference for the capacity of the battery.

Answer 2

Something analogous to what you have in mind is possible with a plate capacitor

In the charged state one plate is depleted of some of the electrons, creating a net positive charge, and the opposite plate is electron enriched, creating a net negative charge.

The plates exert a strong electrostatic attraction upon each other. In other words, in between the plates there is a strong electrostatic field.

So indeed: if you do work to increase the distance between the plates that work done goes into increase of the total potential difference between the plates.

This is valid only in approximation, the approximation is for cases where the distance between the plates remains very small compared to the area of the plates.

An electrostatic field manifests itself in the form of volts per unit of distance. Hence given a particular amount of charge on the plates: a larger gap between the plates corresponds to a larger overal voltage.

Again, this is valid only for small gap between the plates.

Conversely: if the gap is huge, say, twice the diameter of the plates, then the electrostatic attraction will be more like the electrostatic attraction between two point charges, and then the electrostatic attraction is down to the general inverse square force law.

Inverse square force law: proportional to $\frac{1}{r^2}$