Potential Difference between Two Points due to a Charge

The potential difference between any two points is nothing but the work done in joules per coulomb required to move a coulomb of charge between the two points. The force on a charge in the field is measured by electric field intensity which is equal to the force in newtons per coulomb on a coulomb charge at the point considered and is measured in volts per meter.

       Consider a long straight wire carrying positive charge of q c/m as shown in the Fig. 1.

Fig. 1

       Consider two points P₁ and P₂ located at a distance of  D₁ and D₂ from centre of wire. There is positive charge on wire which will repel when a positive charge is placed in the field. If we want to move charge from point P₂ to P₁ then work must be done on positive charge. Here P₁ is at higher potential than P₂. If the charge moves from P₁ to P₂, it expends energy which is nothing but voltage drop from P₁ to P₂. The path followed does not affect the potential difference.

       In order to find the voltage drop from P₁ to P₂ is to obtain the voltage between equipotential surfaces passing through P₁ and P₂.

       The voltage drop between P₁ and P₂ is,

       The voltage drop between two points may be either positive or negative depending upon the charge causing the potential difference is positive or negative. It also depends upon whether the voltage drop is computed from a point near the conductor to a point far away or vice versa.