question_answer

An electric dipole coincides on Z-axis and its mid-point is on origin of the coordinate system. The electric field at an axial point at a distance z from origin is \[{{E}_{(z)}}\] and electric field at an equatorial point at a distance y from origin is \[{{E}_{(y)}}.\]Here 2 = y > a, so \[\left| \frac{{{E}_{(z)}}}{{{E}_{(y)}}} \right|\]is equal to

A) 1                                               

B) 4   

C) 3                                             

D) 2

Correct Answer: D

Solution :

The magnitude of electric field at an axial point Mat a distance z from the origin is given by \[\left| {{E}_{z}} \right|=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{2pz}{{{({{z}^{2}}-{{a}^{2}})}^{2}}}\] For\[z>>a,\left| {{E}_{z}} \right|=\frac{2p}{4\pi {{\varepsilon }_{0}}{{z}^{3}}}\] and, magnitude of electric field at a equatorial point N at a distance y from origin (0,0) is given by For \[\left| {{E}_{y}} \right|=\frac{p}{4\pi {{\varepsilon }_{0}}{{({{y}^{2}}-{{a}^{2}})}^{3/2}}}\] For\[y>>a,\left| {{E}_{y}} \right|=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{p}{{{y}^{3}}}\] For\[z=y>>a\therefore \left| \frac{{{E}_{y}}}{{{E}_{y}}} \right|=2\]