Page 10 - Electrostatics-11
P. 10
© GC Shiba
let us consider a point P in the electric field of +Q charge at a distance r. We
want to find electric potential energy at point P. Put +q charge at point P.
The electric force acting at a point P according to Coulomb's formula is
= Where is permittivity of the free space.
4 2 0
0
Now +q charge is displaced by very small distance dr towards +Q charge then
⃗ ⃗⃗⃗⃗⃗
work done (dw) = .
= F dr cos180 0
= - F dr
= −
4 2
0
Now, total work done in displacing +q 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 energy (U).
9 Electrostatics
