Q. 224.3( 7 Votes )
Figure 2.34 shows
The diagram is given as:
X Y Z
The given charges of same magnitude placed at points X, Y, and Z respectively, forms an electric quadrupole.
Where, charge + q is at point X, charge -2q is at point Y, and charge + q is at point Z.
The point P is at a distance r from point Y.
Here, XY = YZ = a
So, YP = r, PX = r + a, PZ = r-a.
The electrostatic potential due to the system of three charges at point P is given by,
Then a/r<<1 which implies a2/r2 is negligible so it can be ignored,
Thus, potential becomes,
Relation of potential due to quadrupole with r is V1/r3
However, for a dipole it is V1/r2
And for a monopole it is V1/r
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