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 find the ratio of the outgoing electric flux through a sphere and a cube, both containing the same charge of 1 coulomb at their center.

### Step-by-Step Solution:

1. **Understand Gauss's Law**:
Gauss's Law states that the electric flux (Φ) through a closed surface is directly proportional to the charge (Q) enclosed within that surface. Mathematically, it is given by:
\[ \Phi = \frac{Q}{\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

2. **Identify the Charge and Surfaces**:
We have a charge \( Q = 1 \, \text{coulomb} \) located at the center of:
- A sphere of radius \( 10 \, \text{cm} \)
- A cube with a side of \( 20 \, \text{cm} \)

3. **Calculate the Electric Flux through the Sphere**:
Using Gauss's Law for the sphere:
\[ \Phi_s = \frac{Q}{\epsilon_0} = \frac{1}{\epsilon_0} \]

4. **Calculate the Electric Flux through the Cube**:
Similarly, for the cube:
\[ \Phi_c = \frac{Q}{\epsilon_0} = \frac{1}{\epsilon_0} \]

5. **Find the Ratio of the Outgoing Flux**:
Now, we need to find the ratio of the outgoing flux through the sphere to that through the cube:
\[ \frac{\Phi_s}{\Phi_c} = \frac{\frac{1}{\epsilon_0}}{\frac{1}{\epsilon_0}} = 1 \]

6. **Conclusion**:
The ratio of the outgoing electric flux through the sphere and the cube is:
\[ \text{Ratio} = 1 \]

### Final Answer:
The ratio of outgoing flux through the sphere and the cube is \( 1 \).

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