The magnitude of electric field E in the annu | vedclass

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(C) For a cylindrical capacitor with inner radius $a$ and outer radius $b$,the electric field $E$ at a distance $r$ (where $a < r < b$) from the axis

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Varies as $1/r$,where $r$ is the distance from the axis

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(C) For a cylindrical capacitor with inner radius $a$ and outer radius $b$,the electric field $E$ at a distance $r$ (where $a Consider a Gaussian surface in the form of a cylinder of radius $r$ and length $L$.The total charge enclosed is $q = \lambda L$,where $\lambda$ is the linear charge density.According to Gauss's Law,$\oint E \cdot dA = \frac{q_{enclosed}}{\varepsilon_0}$.$E(2\pi r L) = \frac{\lambda L}{\varepsilon_0}$.Thus,$E = \frac{\lambda}{2\pi \varepsilon_0 r}$.This shows that the magnitude of the electric field $E$ varies inversely with the distance $r$ from the axis,i.e.,$E \propto 1/r$.

The magnitude of electric field $E$ in the annular region of a charged cylindrical capacitor:

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