A charge of 1 coulomb is located sat the centre of a sphere of raidus 10 cm and a cube of side 20 cm. The ratio of outgoing flux the sphere and cube will be

Options

A. More than one
B. Less than one
C. One
D. Nothing certain can be said

Answer

To solve the problem, we need to determine the ratio of the electric flux through a sphere and a cube when a charge of 1 coulomb is placed at their centers.

### Step-by-Step Solution:

1. **Understanding Electric Flux**:
The electric flux (Φ) through a closed surface is given by Gauss's Law, which states:
\[ \Phi = \frac{Q_{\text{inside}}}{\epsilon_0} \]
where \( Q_{\text{inside}} \) is the charge enclosed by the surface and \( \epsilon_0 \) is the permittivity of free space.

2. **Calculate Flux through the Sphere**:
- The charge \( Q_{\text{inside}} \) for the sphere is 1 coulomb.
- Therefore, the electric flux through the sphere (Φ_s) is:
\[ \Phi_s = \frac{1 \, \text{C}}{\epsilon_0} \]

3. **Calculate Flux through the Cube**:
- Similarly, the charge \( Q_{\text{inside}} \) for the cube is also 1 coulomb.
- Thus, the electric flux through the cube (Φ_c) is:
\[ \Phi_c = \frac{1 \, \text{C}}{\epsilon_0} \]

4. **Finding the Ratio of Fluxes**:
- Now, we can find the ratio of the outgoing flux from the sphere to that from the cube:
\[ \frac{\Phi_s}{\Phi_c} = \frac{\frac{1}{\epsilon_0}}{\frac{1}{\epsilon_0}} = 1 \]

5. **Conclusion**:
The ratio of outgoing flux from the sphere to the cube is:
\[ \text{Ratio} = 1 \]