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The magnitude of electric field vecE in ...

The magnitude of electric field `vecE` in the annular region of a charged cylindrical capacitor.

A

is same throughout

B

is higher near the outer cylinder than near the inner cylinder

C

varies as `1//r`, where r is the distance from axis

D

varies as `1//r^2` where r is the distance from the axis.

Text Solution

Verified by Experts


Let `lamda` be the charge per unit length. Let us consider a gaussian surface (dooted cylinder) (fig) Applying gauss's law, we get
`phi=ointvec(E).vec(ds)=(lamdal)/(epsilon_(0))`
For the flat portions of the haussian surface, the angle between electric field and surface `90^(@)` hence flux through flat portions is zero. By symmetery the electric field on the curved surface is the same thorughout the angles between `vecE` and `vec(ds)` is `0^(@)` (for curved surface)
`Eintds=(lamdal)/(epsilon_(0))orExx2pirl=(lamdal)/(epsilon_(0))or E=(lamda)/(2piepsilon_(0)r)`
or `Eprop(1)/(r)`
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