Question
Two-point charges $8\mu C$ and $- 2\mu C$ are located at $x = 2\text{ }cm$ and $x = 4\text{ }cm$, respectively on the x -axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is $\_\_\_\_$ .
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Solution
Sol. [Key Concept: Gauss's law: flux $\propto$ enclosed charge; compare the charge inside each sphere.]
For sphere with radius 3 cm and center origin
$$\phi_{1} = \frac{q_{en}}{\varepsilon_{0}} = \frac{8\mu C}{\varepsilon_{0}} $$for sphere of radius 5 cm
$${\phi_{2} = \frac{q_{en}}{\varepsilon_{0}} = \frac{(8 - 2)\mu C}{\varepsilon_{0}} = \frac{6\mu C}{\varepsilon_{0}} }{\frac{\phi_{1}}{\phi_{2}} = \frac{8}{6} = \frac{4}{3} = 1.33 }{\frac{\phi_{1}}{\phi_{2}} = 1.33 }$$
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