A hollow cylinder has a charge ' q ' coulomb within it. If ' φ ' is… | MHT CET 2025 (20 Apr, Shift 2)

Q21MHT CET 2025 · 20 APR · SHIFT 2Easy

Electric Flux & Gauss's Law

A hollow cylinder has a charge ' $q$ ' coulomb within it. If ' $\phi$ ' is the electric flux in unit of V-m associated with the curved surface C, the flux linked with the plane surface ' $A$ ' in unit of V-m will be [ $\varepsilon_0 =$ permittivity of free space]0

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Answer: (c)

Total flux through the closed cylinder: $\phi_A + \phi_B + \phi_C = \dfrac{q}{\varepsilon_0}$ .
With the charge at the centre, the two flat faces get equal flux: $\phi_A = \phi_B$ , and $\phi_C = \phi$ .
$2\phi_A = \dfrac{q}{\varepsilon_0} - \phi \Rightarrow \phi_A = \dfrac{1}{2}\left(\dfrac{q}{\varepsilon_0} - \phi\right)$
So the answer is (c).

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