CBSE Class 12-science Answered
Deduce Coulomb's law from Gauss theorum.
Asked by Aarushi Srivastava | 11 May, 2022, 20:19: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/a24557ebdf29c32fa9c02bb229daa61d627beee4079a65.01522514f8.png)
Gauss theorem states that total electric flux over a closed surface equals enclosed charge
divided by permittivity of enclosed medium.
Let us consider a sphere of radius R has charge at centre of sphere.
Then by Gauss theorem ,
.....................(1)
![begin mathsize 14px style surface integral E times d A space equals space q over epsilon end style](https://images.topperlearning.com/topper/tinymce/cache/490892c39410953a10a18dbe8e7ec0d6.png)
Where E is uniform electric field intensity over the surface of sphere , q is enclosed charge
and ε is permittivity of medium
Since Electric field intensity E is uniform over the surface of sphere ,
we can write the RHS of eqn.(1) as
![begin mathsize 14px style surface integral E times d A end style](https://images.topperlearning.com/topper/tinymce/cache/13b93e420356efbb9c0160f5b54de67f.png)
where 4π R2 is surface area of sphere.
Using eqn.(1) and (2) , we write
E × 4π R2 = ( q / ε )
Hence Electric field E is written as
![begin mathsize 14px style E space equals space fraction numerator q over denominator 4 pi epsilon space R squared end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/a640b5e31822c125952d3fa1f41d4fa5.png)
Above expression equals electric field at a distance R from a charge q.
Since electric field is force / unit charge , force experienced by a test charge q' at a distance R
from the given charge q is written as
![begin mathsize 14px style F space equals space q apostrophe space E space equals space fraction numerator q apostrophe space q over denominator 4 pi epsilon space R squared end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/e6da76160e93ed6f405f52163597d755.png)
Above expression is Columbs law that gives electrical force between two charges q and q'
that are separated by a distance R
Answered by Thiyagarajan K | 11 May, 2022, 23:13: PM
Concept Videos
CBSE 12-science - Physics
Asked by Aarushi Srivastava | 11 May, 2022, 20:19: PM
CBSE 12-science - Physics
Asked by rajwindersarao111 | 21 Jul, 2020, 08:50: AM
CBSE 12-science - Physics
Asked by sarojinib726 | 29 Jun, 2020, 07:57: AM
CBSE 12-science - Physics
Asked by my3shyll | 17 May, 2018, 08:00: AM
CBSE 12-science - Physics
Asked by Topperlearning User | 16 Apr, 2015, 10:41: AM
CBSE 12-science - Physics
Asked by Topperlearning User | 16 Apr, 2015, 10:42: AM
CBSE 12-science - Physics
Asked by Topperlearning User | 16 Apr, 2015, 10:42: AM
CBSE 12-science - Physics
Asked by Topperlearning User | 16 Apr, 2015, 10:46: AM
CBSE 12-science - Physics
Asked by Topperlearning User | 16 Apr, 2015, 10:47: AM
CBSE 12-science - Physics
Asked by Topperlearning User | 16 Apr, 2015, 10:52: AM