Electric Charges and Fields - Result Question 39
39. A hollow cylinder has a charge $q$ coulomb within it. If $\phi$ is the electric flux in units of voltmeter associated with the curved surface $B$, the flux linked with the plane surface $A$ in units of voltmeter will be
[2007]
$ \text{ B } $
(a) $\frac{q}{2 \varepsilon_0}$
(b) $\frac{\phi}{3}$
(c) $\frac{q}{\varepsilon_0}-\phi$
(d) $\frac{1}{2}(\frac{q}{\varepsilon_0}-\phi)$
Show Answer
Answer:
Correct Answer: 39. (d)
Solution:
- (d) Since $\phi _{\text{total }}=\phi_A+\phi_B+\phi_C=\frac{q}{\varepsilon_0}$,
where $q$ is the total charge.
As shown in the figure, flux associated with the curved surface B is $\phi=\phi_B$
Let us assume flux linked with the plane surfaces $A$ and $C$ be
$\phi_A=\phi_C=\phi^{\prime}$
Therefore,
$\frac{q}{\varepsilon_0}=2 \phi^{\prime}+\phi_B=2 \phi^{\prime}+\phi$ $\Rightarrow \phi^{\prime}=\frac{1}{2}(\frac{q}{\varepsilon_0}-\phi)$
