CBSE Class 12-science Answered
Please solve this question
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Asked by shinghip6 | 17 Jul, 2022, 16:36: PM
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Electric dipole consists of two charges of equal magnitude but opposite sign that are separated by a small distance
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/309271cd698bdb54c96f3c4af5c4f39962d4ce5ce1ca34.44803354f1.png)
Electric dipole moment
is the product of charge q and distance d .
![begin mathsize 14px style p with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/02ce4eee15602c5766a8f3d4c0ac7978.png)
Electric dipole moment
is vector quantity thta has direction from negative charge to positive charge
![begin mathsize 14px style p with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/02ce4eee15602c5766a8f3d4c0ac7978.png)
![begin mathsize 14px style p with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/02ce4eee15602c5766a8f3d4c0ac7978.png)
![begin mathsize 14px style d with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/d7e3c99b3a1bb179e2d555fa37981ce3.png)
--------------------------------
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/0206751cb963a590a563a58320bdfaba62d4d33fb42270.52418872f1.png)
Let us consider a point P on the axis passing through mid point of dipole. Let the point P be at a distance z from centre .
At the point P , two charges are at equal distance from P .
Since the charges are equal in magnitude and opposite in direction, potential at P is zero.
Electric field at P due to positive charge is E+ as shown in figure .
Similarly electric field at P due to negative charge is E- as shown in figure .
Magnitude E of E+ and E- are same because magnitude of charge and distances are equal for both fields.
Resultant field ER is given as
![begin mathsize 14px style E subscript R space equals space 2 space cross times space K space cross times fraction numerator q over denominator open parentheses z squared plus d squared over 4 close parentheses end fraction cross times cos theta end style](https://images.topperlearning.com/topper/tinymce/cache/88d97cc542838560bc291c3201ea6b0b.png)
where K = 1 / ( 4πεo ) is the coulomb's constant
where cosθ is given as
![begin mathsize 14px style cos theta space equals space fraction numerator d divided by 2 over denominator square root of z squared plus begin display style d squared over 4 end style end root end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/74e61b9494bdbf3a069e75b4f4b61e20.png)
Hence resultant electric field is written as
![begin mathsize 14px style E subscript R space equals space space K space cross times fraction numerator q space d over denominator open parentheses z squared plus d squared over 4 close parentheses to the power of 3 divided by 2 end exponent end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/e0382231dc243258ec8a7076133acdd6.png)
If we use the definition of dipole moment " p = q d " and consider d << z , then resultant field will become
![begin mathsize 14px style E subscript R space equals space space K space cross times p over z cubed end style](https://images.topperlearning.com/topper/tinymce/cache/5da646d7121ad8f8710a413a51dfab22.png)
Answered by Thiyagarajan K | 18 Jul, 2022, 09:32: AM
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