Page 11 - Electrostatics-11
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© GC Shiba
∴ =
4
0
This is the required expression for electric potential energy.
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.
4 2 0
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
1
= ∫ − 2
0
2 4
10 Electrostatics
