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

Solution

Physics sir · 4 steps

Gauss's law only asks what is inside each cube, and the big cube holds the small cube's charge too.

1. Gauss's law. The total flux through any closed surface depends only on the charge it encloses: φ = q_(enc)/ε₀. The size and shape of the surface do not matter.
2. Inner cube C1. Only the charge 2Q sits inside C₁. The 3Q lies outside it, so it adds nothing to the net flux through C₁. That gives φ₁ = 2Q/ε₀.
3. Outer cube C2. C₂ surrounds everything: the 3Q in the space between the cubes and the 2Q inside C₁. So q_(enc) = 2Q + 3Q = 5Q and φ₂ = 5Q/ε₀.

   φ₁/φ₂ = (2Q/ε₀)/(5Q/ε₀) = 2/5

4. So. The ratio of flux through C₁ and C₂ is 2 : 5, which is option (c).

The idea to keep. For nested closed surfaces, the outer one encloses every charge inside the inner one as well. Add up all the charge inside a surface before you use φ = q_(enc)/ε₀.

Answer from the NTA final answer key. Solution by PrepWiser.