Question

Figure shows five charged lumps of plastic and a electrically neutral coin. The cross section of a
Gaussian surface s is indicated. What is the net electric flux through the surface​

Answer 1

Given:

Figure shows five charged lumps of plastic and a electrically neutral coin. The cross section of a

Gaussian surface s is indicated.

To find:

Net Electrostatic flux.

Calculation:

Gauss' Theorem states that the net electrostatic flux through a Gaussian surface will always be equal to the enclosed charge divided by the permittivity of free space.

$\boxed{ \bold{ \therefore \: \phi = \dfrac{ q_{enclosed}}{ \epsilon_{0} } }}$

$\sf{ = > \: \phi = \dfrac{ q1 + q2 + q3}{ \epsilon_{0} } }$

$\sf{ = > \: \phi = \dfrac{ (q4 + 3.1 \times {10}^{ - 9} ) + ( - 5.9 \times {10}^{ - 9} ) + ( - 3.1 \times {10}^{ - 9} ) }{ \epsilon_{0} } }$

$\sf{ = > \: \phi = \dfrac{ (q4 )+( 3.1 \times {10}^{ - 9} ) - ( 5.9 \times {10}^{ - 9} ) - (3.1 \times {10}^{ - 9} )}{ \epsilon_{0} } }$

$\sf{ = > \: \phi = \dfrac{ q4 - (5.9 \times {10}^{ - 9} )}{ \epsilon_{0} } }$

$\sf{ = > \: \phi = \dfrac{ q4 -( 5.9 \times {10}^{ - 9}) }{ 8.85 \times {10}^{ - 12} } }$

So, final answer is:

$\boxed{ \bold{ \: \phi = \dfrac{ q4 -( 5.9 \times {10}^{ - 9}) }{ 8.85 \times {10}^{ - 12} }N{C}^{ - 1} {m}^{2} }}$