Question

Calculate the potential difference between 2 terminals of the battery, if $100$ Joules of work is required to transfer $20\,C$ of charge from one terminal of the battery to the other.

Answer 1

We know that potential difference is the work done per unit charge and this relation is given by $W = qV$. In this question, this is all that is needed, we substitute the values of work done and charge to get the potential difference.

Complete step by step answer:
Let us look at the definition of potential difference : Potential difference is defined as work done to move unit positive charge from one point to another point. We can use this definition to solve the above question.
Given: Work done to transfer the charge is 100 J and the charge given is 20 C.
Hence substituting these in the equation
$W = qV$
$\Rightarrow 100 = 20V$
$\Rightarrow \dfrac{{100}}{{20}} = V$
$\therefore V = 5V$.

Hence the potential difference between the terminals of the battery is 5 V.

Additional information: In general if a unit positive charge is given a displacement $\delta l$ in a direction at an angle $\theta$. Workdone is given by $\delta w = - E\delta l\cos \theta$ where $E$= electric field.

Note: Work Done in moving a charged particle from one point to another in an electrostatic field depends only on initial and final points, and not the path covered in between the 2 point;$W = {V_f} - {V_i}$ Where ${V_f}$ is final potential and ${V_i}$ is initial potential and $W$ is work done. Remember that potential due to positive charge is positive and potential due to negative charge is negative.