Question

What is the total electric flux leaving the surface of the sphere?

• A. $1.63\times {10}^{2}N{m}^2/C$
• B. $1.63\times {10}^{4}N{m}^2/C$
• C. $1.63\times {10}^{6}N{m}^2/C$
• D. $1.63\times {10}^{8}N{m}^2/C$

Answer 1

The correct option is D $1.63\times {10}^{8}N{m}^2/C$

Charge,$q$=surface charge density $\left(\sigma \right)\times$ area $\left(A\right)$

$⟹q=\sigma \times 4\pi r^2$

$⟹q=\sigma \times 4\pi {\left(\frac{d}{2}\right)}^2$ where $d=diameter$

$⟹q=80\times {10}^{-6}\times 4\pi \times {\left(\frac{2.4}{2}\right)}^2$

$⟹q=1.45\times {10}^{-3}C=1.45mC$

Hence, flux$=\frac{q}{{ϵ}_o}=\frac{1.45\times {10}^{-3}}{8.85\times {10}^{-12}}$

$⟹\varphi =1.63\times {10}^{8}N{m}^2/C$

Answer-(D)