Question 3: What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential energy?

ANSWER

Relationship between Voltage and energy

Voltage, a popular name for potential difference, is defined as ‘the work done in moving a unit positive charge from one point to the other against the electric field’.

Consider an electric field due to source charge as shown in the figure. Also, consider two points A and B in this field. If a unit positive charge is brought to point A from somewhere outside the field, work must be done on it. This work is stored in the charge as electric potential energy and is W = U = V = potential at point A. However, if the charge is not a unit charge but of some other value, q, then the energy stored in the charge is U₁ = qV₁.      …       (1)
This equation gives the relation between potential and energy.

Similarly, if the same amount of charge is taken to point B, from outside the field, the amount of work done and hence the energy stored in the charge, will be different. Let it is W2, so that U₂ = qV₂.     …     (2)

Potential difference and potential energy

Now we have found the potentials and energies at points A and B. These will not be equal as different amounts of work has been done in bringing charge q to these points. Now if we place the charge q at point A and take it slowly to point B, the amount of work done will be W₂ – W₁ = U₂ – U₁ = qV₂ – qV₁ OR ΔU = q ΔV Since q is constant, therefore, ΔU is proportional to ΔV. This is the relation between potential difference and the P.E stored in a charge between the two points.