CBSE Class 12-science Answered
Obtain the ratio of Electric field formed by an ideal dipole at points lying on axial and equatorial axis.
Asked by avaneesh1162 | 12 Jun, 2021, 11:06: AM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/f3fc970b8eb3e4655e1bce44a7c48d1d60c47168320964.06715488f4.png)
Let a dipole consists of charges +q and -q that are separated by a distance d is placed at origin of
X-Y coordinate system so that mid point of dipole coinicides with origin.
Electric field at a point x = r on x-axis is given as
![begin mathsize 14px style E subscript x space equals space E subscript plus space minus space E subscript negative space space end subscript equals space left parenthesis space K space cross times space q space right parenthesis space open parentheses 1 over open parentheses r minus begin display style d over 2 end style close parentheses squared space minus space 1 over open parentheses r space plus begin display style d over 2 end style close parentheses squared close parentheses space end style](https://images.topperlearning.com/topper/tinymce/cache/b51d402a5263dd9e03017239efbe6bd7.png)
![begin mathsize 14px style E subscript x space equals space fraction numerator left parenthesis space K space cross times space q space right parenthesis over denominator open parentheses r squared space minus space begin display style d squared over 4 end style close parentheses squared end fraction cross times left parenthesis 2 space r space d right parenthesis end style](https://images.topperlearning.com/topper/tinymce/cache/3ed3c468a3f4e6aa33e85571f160760a.png)
Where K = 1/ (4πεo ) is Coulomb's constant
if we consider dipole moment p = ( q × d ) and r >> d/2 , then eqn.(1) is written as
Ex = K × [ ( 2 p ) / r3 ] ............................ (2)
Electric field at a point y = r on y-axis is given as
Ey = 2 E cosθ .................................(3)
Where E is given as
![begin mathsize 14px style E space equals space E subscript plus space equals space E subscript minus space equals space K space cross times fraction numerator q over denominator open parentheses r squared space plus space begin display style d squared over 4 end style close parentheses end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/69214aec05740ffa7a7745c35c435104.png)
Hence we get Ey as ,
.........................(4)
![begin mathsize 14px style E subscript y space equals space 2 space cross times K space cross times fraction numerator q cross times space left parenthesis d divided by 2 right parenthesis over denominator open parentheses r squared space plus space begin display style d squared over 4 end style close parentheses to the power of 3 divided by 2 end exponent end fraction space equals space K cross times p over r cubed end style](https://images.topperlearning.com/topper/tinymce/cache/4ea47d3a58e3847d5bf96ae9a912d6c5.png)
In above expression , we used the approximation r >> d and dipole moment p = ( q × d )
From eqn.(2) and eqn.(4) , we get ( Ex / Ey ) = 2
Answered by Thiyagarajan K | 12 Jun, 2021, 14:59: PM
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