Question

A hollow cylinder has a charge of 'q' C within it. If 𝜙 is the electric flux associated with the curved surface B, the flux linked with the plane surface A will be ______.

Options

• \[\frac {𝜙}{3}\]

• \[\frac {q}{ε_0}\] - 𝜙

• \[\frac {q}{3ε_0}\]

• \[\frac {1}{2}\]\[\left(\frac{q}{\varepsilon_{0}}-\phi\right)\]

Answer 1

A hollow cylinder has a charge of 'q' C within it. If 𝜙 is the electric flux associated with the curved surface B, the flux linked with the plane surface A will be \[\frac {1}{2}\]\[\left(\frac{q}{\varepsilon_{0}}-\phi\right)\].

Explanation:

As per Gauss' law the net flux through closed surface is,

\[\phi_\mathrm{A}+\phi_\mathrm{B}+\phi_\mathrm{C}=\frac{\mathrm{q}}{\varepsilon_0}\]

Due to symmetry, the same flux passes through plane surface A and C, i.e., 𝜙_A = 𝜙_C

\[\therefore\] 2𝜙_A + 𝜙 = \[\frac {q}{ε_0}\]   ...(Given: 𝜙_B = 𝜙)

\[\phi_\mathrm{A}=\frac{1}{2}\left(\frac{\mathbf{q}}{\varepsilon_0}-\phi\right)\]