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1. Electric Charges and Fields
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A hollow cylinder has a charge $q$ coulomb within it. If $\phi $ is the electric flux in units of voltmete associated with the curved surface $B$ , the flux linked with the plane surface $A$ in units of volt-meter will be
A
$\frac{1}{2}\,\left( {\frac{q}{{{ \in _0}}}\, - \,\phi } \right)$
B
$\frac {q}{2\, \in_0}$
C
$\frac {\phi }{3}$
D
$\frac {q}{\in _0} - \phi $
Solution
${\phi _{{\rm{Total }}}} = {\phi _A} + {\phi _B} + {\phi _C} = \frac{q}{{{ \in _0}}};$
$\therefore \phi_{\mathrm{B}}=\phi$ and $\phi_{\mathrm{A}}=\phi_{\mathrm{C}}=\phi^{\prime}$ [assumed]
$\therefore 2{\phi ^\prime } + \phi \frac{q}{{{ \in _0}}} \Rightarrow {\phi ^\prime } = \frac{1}{2}\left( {\frac{q}{{{ \in _0}}} – \phi } \right)$
Standard 12
Physics
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