Question

C1 and C2 are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in figure. The ratio of electric flux passing through C1 and C2 is :

• A. 2 : 5
• B. 5 : 2
• C. 2 : 3
• D. 3 : 2

Answer 1

The Correct Option is A

To determine the ratio of electric flux through two concentric hollow cubes, C1 and C2, Gauss's Law is applied. This law states that electric flux (\(\Phi\)) through a closed surface is directly proportional to the enclosed charge, expressed as: \(\Phi = \frac{Q_{\text{enclosed}}}{\varepsilon_0}\).

For cube C1, the enclosed charge is \(2Q\). Thus, the electric flux through C1 is: \(\Phi_1 = \frac{2Q}{\varepsilon_0}\).

For cube C2, the enclosed charge comprises the charge within C1 plus its own charge, totaling \(2Q + 3Q = 5Q\). Consequently, the electric flux through C2 is: \(\Phi_2 = \frac{5Q}{\varepsilon_0}\).

The ratio of electric flux through C1 to C2 is calculated as: \(\frac{\Phi_1}{\Phi_2} = \frac{\frac{2Q}{\varepsilon_0}}{\frac{5Q}{\varepsilon_0}} = \frac{2}{5}\).

Therefore, the ratio of electric flux passing through C1 to C2 is \(2 : 5\).