1.

A square sheet of side 'a' is lying parallel to XY plane at z = a. The electric field in the region is \(\vec E=cz^2\hat k\). The electric flux through the sheet is :(a) a4c(b) \(\frac{1}{3}\)a3c(c) \(\frac{1}{3}\)a4c(d) 0

Answer»

Option : (a) a4c

Given,

\(\vec E\) = \(cz^2\hat k\) 

z = a

\(\phi\) = ?

\(\phi\) = \(\int \vec E.d\vec s\)

∵ ds = \(dxdy\,\hat k\)  

\(\phi\) = \(\int(cz^2)\hat k\,dx\,dy\,\hat k\)

\(\phi\) = \(\int\limits_0^zcz^2 dx\,dy\) 

\(\phi\) = \(cz^2\)\(\int\limits_0^zdx\,\int\limits_0^zdy\)

\(\phi\) = \(cz^2\)\([x]_0^z\) \([y]_0^z\)

\(\phi\) = \(cz^2\)[z].[z]

\(\phi\) = cz4

\(\phi\) = ca4 (∵ z = a given)

∴ Option : (a) is correct



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