Page 13 - Electrostatics 11

Grade 11 © GC Shiba

∴ =
4
0

This is the required expression for electric potential energy.

☻ Use Coulomb's law to define potential difference between two
points near a static charge. Also derive expression for it.

Electric potential difference:

Electrical potential difference between two points in the electric field is defined as

the amount of work done in taking unit positive charge from one point to another
point.

r2 A P B
+Q
r1 (+1)

r

Consider two points A and B at distances r1 and r2 from +Q charge. We want
to find p.d. between points A & B. Let us take another point P at a distance f of +Q

charge on the same line. Put +1 charge at point P.

Electric force at point P according to Coulomb's law is

= Where is permittivity of the free space.
0
4 2
0
Now +1 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 +1 charge from B to A is integral of dw

between limit r2 to r1.

1
∴ W = ∫
2

13 Electrostatics