CBSE Class 12-science Answered
obtain expression for force between plates of a charged parallel plate capacitor
Asked by bmahalik21 | 05 Mar, 2023, 20:23: PM
Electric field E near capacitor plate , E = σ / ( 2 εr εo )
where σ = Q/A is surface charge density on capacitor plate. Q is total charge o plate and A is area.
εr is dielectric constant of material between capacitor plates. If capacitor plates are air filled ,then εr = 1
εo is permittivity of free space.
Hence electric field E becomes , ![begin mathsize 14px style E space equals space fraction numerator Q over denominator 2 space A space epsilon subscript r space epsilon subscript o end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/abefb4a713f1667bee4c37f149b347dd.png)
![begin mathsize 14px style E space equals space fraction numerator Q over denominator 2 space A space epsilon subscript r space epsilon subscript o end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/abefb4a713f1667bee4c37f149b347dd.png)
Force F on charges of other plate , F= ( Q ×E )
![begin mathsize 14px style F space equals space fraction numerator Q squared over denominator 2 space cross times space A space cross times epsilon subscript r cross times space epsilon subscript o space end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/3fb09982c27d07ac918fe40d0109cc9b.png)
Normally we do not measure , charge on capacitor plates .
We know the capacitance C of capacitors and applied electrical potential difference V across capacitor plates .
Q = C × V .
Hence force between capacitor plates becomes
![begin mathsize 14px style F space equals space fraction numerator C squared space cross times space V squared over denominator 2 space cross times space A space cross times epsilon subscript r cross times space epsilon subscript o space end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/bb0a33c3f52ed2d951138d03ff9d931d.png)
Answered by Thiyagarajan K | 05 Mar, 2023, 22:12: PM
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