Obtain an expression for electrostatic potential energy at a point on the equotorial line of an electrostatic potential energy at a point on the equatorial line of an electric dipole
Answers
“Electric potential due to an electric dipole in broad side on position or transversal position”:
Consider AB is electric dipole made up by two point charges -q and +q and of length 2a. Thus its dipole moment is P = 2a.q ,
we are to find the electric potential due to this dipole in in its broad side on position at distance r from its midpoint O. let the electric constant of a medium around the dipole is K .
In right angle ΔAOP
By Pythagoras theorem
AP² = OP² + OA²
AP² = r² + a²
AP = (r² + a²)½
Here, AP = BP
Hence, BP = (r² + a²)½
Electric potential due to +q charge of electric dipole at point P is ---
V1 = 1/4π£oK × +q/BP
V1 = 1/4π£oK × +q/(r²+a²)½ volt
similarly, Electric potential due to -q charge of electric dipole at point P is-----
V2 = 1/4π£oK × -q/AP
V2 = 1/4π£oK × -q/(r²+a²)½ volt
Thus, the total electric potential due to dipole at point P will be ---
V = V1 + V2
Putting value of V1 and V2
V = [ 1/4π£oK × +q/(r²+a²)½ ] +
[ 1/4π£oK × -q/(r²+a²)½ ]
V = [ 1/4π£oK × q/(r²+a²)½ ] --
[ 1/4π£oK × q/(r²+a²)½ ]
V = 0
Hence, Electric potential due to electric dipole in its broad side position is zero
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