Question

How much energy is given to each coulomb of charge passing through a $6V$ battery?

Answer 1

A uniform electric field (or a constant electric field) can be generated by an infinite uniformly charged plane. A battery also generates an approximately constant electric field around itself when it sets up a potential difference between two parts of a wire. Understanding this concept, we shall find the energy given to each charge.

Complete step-by-step solution:
When a charge has to move within such an electric field, some work is done on the charge due to this motion. In order to find the work done, we calculate the force experienced by the charge while it is in the electric field as work done on charge is equal to the force applied on its displacement within the electric field. Now, if work is done on a charge for its movement, energy is also given to the charge. This energy is measured in terms of the potential difference of the battery and the amount of charge itself.

The electric energy, $E$ is expressed as:
$E=q\Delta V$
Where,
$q=$ total charge
$\Delta V=$ potential difference of the cell or battery

Here, we are given $q=1C$ (or one coulomb) and potential difference of battery, $\Delta V=6V$,

Thus, energy, $E=\left( 1 \right)\left( 6 \right)$
$\Rightarrow E=6$Joules.

Note:
This energy is also often called the electric potential energy and is always measured relative to a point in the electric field. Also, a charge experiences force because an electric field consists of positive charge at one end and negative charge on the other. Thus, according to the polarity of the charge, it attracted or repelled by both sides respectively.