Consider a charge q is placed at a point. Let B and C be two points where point B is closer to q than C. If a charge q is brought from infinity to C or from infinity to B work done respectively be WC and WB.
The potential at points B and C respectively:
VB = WB/q
VC = WC/q
The potential difference is the difference in potentials VB and VC:
VB - VC = (WB - WC)/q
WB - WC is the work done in carrying charge from point C to B.
Thus, potential difference between two points B and C is equal to the amount of work done in moving a unit charge from point C to point B.
V = W/q
The potential difference (pd) between two points of a conductor is said to be 1 volt if 1 joule of work is done in moving 1 coulomb of charge from one point to another. Potential difference is a scalar quantity. It is measured using an instrument voltmeter. Voltmeter is always connected in parallel across which you have to measure the potential difference.
Example 1: How many electrons make one coulomb?
Let n electrons make 1 C.
Charge on 1 electron is 1.6 × 10-19 C.
Charge, q = +n|e|
n = q/e
= 1/(1.6 × 10-19)
= 6.25 x 1018 electrons
Example 2: Calculate the work done in moving a charge of 3 C across two points having a potential difference of 24 V.
Given, q = 3 C, V = 24 V, W = ?
W = qV
= 3 C x 24 V
W = 72 J