Explain the superposition principle for static electric forces and write its general equation.

Explanation

The figure (a) shows that two needle of equal phase oscillating represents two coherent sources. Consider two needles moving periodically up and down in an identical fusion in a trough of water as shown in figure, they produce two water waves.
At a particular point, the phase difference between the displacement produced by each of the waves does not change with time so both sources are called coherent sources.

Figure (b) shows the position of crests (solid circle) and troughs (dashed circles) at a given instant of time.
Now consider a point P according to figure (a) for which `S_(1)P=S_(2)P`
Since waves from `S_(1)` and `S_(2)` will take the same time to travel to the point P with same phase.
The displacement of distance produced by the source at the point P is given by `S_(1)`
`y_(1)=acosomegat` and the displacement produced by the source S, at the point P will be given by `y_(2)=acosomegat` where a= amplitude.
According to superposition principle, the resultant displacement at P.
`y=y_(1)+y_(2)=acosomegat+acosomegat`
`:.y=2acosomegat`
Now intensity of light is proportional to the square of amplitude.
`:.` The intensity produced by each one of the individual source is `I_(0)`, then
`I_(0)prop("amplitude")^(2)" ":.I_(0)propa^(2)`
`:.` The resultant intensity due to superposing of both waves at point P
`Iprop(2a)^(2)` where amplitude =2a
`:.(I)/(I_(0))=(4a^(2))/(a^(2))`
`:.I=4I_(0)` (For constructive interference) and resultant displacement for destructive interference.
`y=y_(1)-y_(2)=acosomegat-acosomegat`
`:.y=0`
`:.` Resultant intensity will be zero at P
(Destructive interference).