CBSE Class 12-science Answered
explain coulambs law give unit and dimensions of electrostatics constant and coulambs law in vector form with superposition principle
![question image](http://images.topperlearning.com/topper/new-ate/top_mob1673270283983318550Screenshot_2023-01-09-18-44-53-00_c37d74246d9c81aa0bb824b57eaf7062.jpg)
Asked by bhatig9772 | 09 Jan, 2023, 18:48: PM
Coulomb's law
Electrostatic force
between two charges q1 and q2 that are separated by a distance d is
![begin mathsize 14px style F with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/65dc93af5d8bab1de7b0096c22f518cb.png)
![begin mathsize 14px style F with rightwards arrow on top space equals space K space fraction numerator q subscript 1 space q subscript 2 over denominator d squared end fraction space r with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/36cc3b430731121df6cb101eedef95eb.png)
where K = 1/(4
) is Coulomb's constant or electrostatic constant and
is unit vector
![begin mathsize 14px style πε subscript straight o end style](https://images.topperlearning.com/topper/tinymce/cache/75586ef52753ee0a8585594378c8d99e.png)
![begin mathsize 14px style r with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/57111c07fb27191d059d2c555091dada.png)
along the direction of line joining charges q1 and q2 .
----------------------------------------
Units of electrosatatic constant K = 1/(4
) is N m2 C-2
![begin mathsize 14px style πε subscript straight o end style](https://images.topperlearning.com/topper/tinymce/cache/75586ef52753ee0a8585594378c8d99e.png)
Dimension of Newton N = M L T-2
Coulomb is current × time . Hence dimension of coulomb = A T-1
Hence dimension of electrostatic constant = M L T-2 × L2 × A T-2 = M L3 T-3
( M is mass , L is length and A is Ampere )
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Coulomb's law in vector form and superposition principle
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/a0f1ed93b98fbb097cdef10e1d7dba0f63bc5560b0a2b9.81823430f5.png)
Let q be the test charge at position vector
as shown in figure.
![begin mathsize 14px style r with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/18d9063f1aa24fc3e615246827a59066.png)
Charge q1 is at position vector
. charge q2 is at position vector
.. So on ....
![begin mathsize 14px style stack r subscript 1 with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/17542093e56806d59109eec21eba8d95.png)
![begin mathsize 14px style stack r subscript 2 with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/ba33c1cb2ffd2cb22517eed8937077f2.png)
Net force
experienced by charge q is
![begin mathsize 14px style F with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/65dc93af5d8bab1de7b0096c22f518cb.png)
![begin mathsize 14px style F with rightwards arrow on top space equals K space sum for i of space space space fraction numerator q space q subscript i over denominator d subscript i end fraction space space stack r subscript i with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/17cd644e1db774ebc8cc574470b092c6.png)
where di =
and
![begin mathsize 14px style open vertical bar stack r subscript i with rightwards arrow on top space minus space r with rightwards arrow on top close vertical bar end style](https://images.topperlearning.com/topper/tinymce/cache/1b47f65cac57b3a28e24134accf08eca.png)
![begin mathsize 14px style stack r subscript i with hat on top space equals space fraction numerator stack r subscript i space with rightwards arrow on top space minus space r with rightwards arrow on top over denominator open vertical bar stack r subscript i space with rightwards arrow on top space minus space r with rightwards arrow on top close vertical bar end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/03c50bb72d65c9b2d925beb5034beaf0.png)
Answered by Thiyagarajan K | 09 Jan, 2023, 23:42: PM
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