A) \[1/d\]
B) \[1/{{d}^{2}}\]
C) \[1/{{d}^{3}}\]
D) \[1/{{d}^{3/2}}\]
Correct Answer: C
Solution :
Electric field of the electric dipole at a point \[P\,(r,\theta )\]is given by \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{3}}}\sqrt{3\,{{\cos }^{2}}\theta +1}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\frac{p}{{{d}^{3}}}\,\sqrt{3\,co{{s}^{2}}\,\theta +1}\] \[[\because \,r=d]\] where p is electric dipole moment. On the axis of the dipole \[\theta ={{0}^{o}}\] \[\Rightarrow \] \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{d}^{3}}}\times \sqrt{3+1}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2p}{{{d}^{3}}}\] \[\Rightarrow \] \[E\alpha \frac{1}{{{d}^{3}}}\]You need to login to perform this action.
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