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Lesson 4, Topic 3
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Electrical Potential

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Electric potential (V) at a point P is the work done in bringing a unit positive charge from infinity to that point in the electric field of another charge.

It is a scalar quantity. Its unit is Joules per Coulomb (J/c)

Electric potential = \( \frac{Work \; done}{charge} \) 

V = \( \frac{w}{q} \) 

If r = distance from infinity to the point charge

F = force of attraction 

 Q1 = Unit charges

 Q2 = attracting charge

Work done = electric potential (V) x  r = F x r

= \( \frac{Q_1 Q_2}{4 \pi \varepsilon_0 r^2} \scriptsize \; \times \; r \)

Q2 = 1

V = \( \frac{Q}{4 \pi \varepsilon_0 r^2} \)

Electrical potential between two points (distance between a and b)

= \( \frac{Q}{4 \pi \varepsilon_0 r^2} \left[ \frac{1}{a} \; – \; \frac{1}{b} \right] \)

Types of electric potential

Zero potential

All potentials around charges are measured using a reference point. Two reference points for charges are 

  • Earth
  • A point at infinity

Equipotential surface

This is an imaginary surface drawn in an electric field such that all point on the surface have the same potential. Their characteristics are as follows:

  • It is the same distance from the source of field
  • The electric lines of force are always perpendicular to the surface
  • The work done in moving a positive charge along the surface is zero
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