Physics - Electrostatics Question with Solution | TestHub

Let${\varphi }_{\text{A}}\text{, }{\varphi }_{\text{B}}\text{ and }{\varphi }_{\text{C}}$are the electric flux linked with$\text{A},\text{B}\text{and C}$.

According to gauss theorem,$\varphi$total$=\frac{\sum q}{{\epsilon }_0}$

${\varphi }_{\text{A}}+{\varphi }_{\text{B}}+{\varphi }_{\text{C}}=\frac{\text{q}}{{\epsilon }_0}$

Since${\varphi }_{\text{A}}={\varphi }_{\text{C}}\text{,}$

$\therefore 2{\varphi }_{\text{A}}+{\varphi }_{\text{B}}=\frac{\text{q}}{{\epsilon }_0}$

or$2{\varphi }_{\text{A}}=\frac{\text{q}}{{\epsilon }_0}-{\varphi }_{\text{B}}$

or$2{\varphi }_{\text{A}}=\frac{\text{q}}{{\epsilon }_0}-\varphi$

(Given${\varphi }_{\text{B}}=\varphi$)

$\therefore {\varphi }_{\text{A}}=\frac{1}{2}\left(\frac{\text{q}}{{\epsilon }_0}-\varphi \right)$