Page 11 - Electrostatics 11

Grade 11 © GC Shiba

= −
4 2
0

Now, total work done in displacing +1 charge from infinity to point P is integral
of dw between limit ∞ to r.

∴ W = ∫
∞

= ∫ − 2
0
∞ 4
1
= − ∫
4 0 ∞ 2

= − ∫ −2
4 0 ∞

−2+1
= − [ ]
4 0 −2 + 1 ∞

1 1
= [ − ]
4 0 ∞

1
= [ ]
4 0

By definition, this work done is electric potential (V).

∴ =
4
0

This is the required expression for electric potential.

Electric potential energy: Electrical potential energy at any point in the

electric field is defined as the amount of work done in taking a given charge from

infinity to the point under consideration.

P dr
⃗⃗
+Q
r (+q)

11 Electrostatics