Question

A charged particle 'q' lies at 'P' and the line PC is perpendicular to the surface of ABC (part of disc). Find the flux passing through the surface ABC.

• A. $\frac{q}{4{\epsilon }_0}$
• B. $\frac{q}{16{\epsilon }_0}$
• C. $\frac{q}{32{\epsilon }_0}$
• D. $\frac{q}{48{\epsilon }_0}$

Answer 1

The correct option is B $\frac{q}{16{\epsilon }_0}$

$E=\frac{q}{4\pi {ϵ}_0{a}^2}$

Area of whole disk$=\pi r^2=\pi (\sqrt{3}a{)}^2=3\pi a^2$

Area of $ABC=\pi r^2\left(\frac{30}{360}\right)=\frac{3\pi a^2}{12}$

$=\frac{1}{12}$ (area of whole disk)

The electric flux through the whole disk,

${\varphi }_T=EA=\frac{q}{4\pi {ϵ}_0{a}^2}\times 3\pi a^2=\frac{3q}{4{ϵ}_0}$

But electric flux, $\varphi =\frac{1}{12}{\varphi }_T=\frac{1}{12}\times \frac{3q}{4{ϵ}_0}$

$=\frac{q}{16{ϵ}_0}$