Find out the magnitude of electric field intensity, E at point (2,0,0) due to a dipole moment, →p=^i+√3^j kept at origin as shown in the figure and also find the potential, V at that point.
[k=14πε0]
A
E=k4,V=k8
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B
E=k3,V=3k2
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C
E=√7k8,V=k4
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D
E=8k3,V=5k2
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Solution
The correct option is CE=√7k8,V=k4
Diagram for the problem:
Magnitude of the dipole moment, p=√12+(√3)2=2Cm
Distance of point from origin , r=2m
Angle of →r from the axis of dipole :
tanθ=√31
⇒θ=60∘
Formula for net electric field E=kpr3√1+3cos2θSubstituting the values,
E=k×223√1+3cos260∘
⇒E=k4√1+34=√7k8
Formula for potential (r,θ) V=kpcosθr2 ⇒V=k×222cos60∘