If R is the radius of a soap bubble and S its surface tension, then the excess pressure inside is

Options

A. `r^-1`
B. `r^-3`
C. `r^2`
D. `r^-2`

Answer

To find the excess pressure inside a soap bubble, we can use the formula derived from the principles of fluid mechanics and the properties of soap bubbles.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a soap bubble with radius \( R \) and surface tension \( S \).
- We need to determine the excess pressure inside the bubble compared to the atmospheric pressure.

2. **Concept of Excess Pressure**:
- The excess pressure inside a soap bubble is due to the surface tension acting on the surface of the bubble.
- A soap bubble has two surfaces (inner and outer), which contributes to the excess pressure.

3. **Using the Formula for Excess Pressure**:
- The formula for the excess pressure \( \Delta P \) inside a soap bubble is given by:
\[ \Delta P = \frac{4S}{R} \]
- Here, \( S \) is the surface tension of the soap solution, and \( R \) is the radius of the bubble.

4. **Substituting the Given Values**:
- In our case, we replace \( S \) with the given surface tension and \( R \) with the radius of the bubble:
\[ \Delta P = \frac{4S}{R} \]

5. **Conclusion**:
- Therefore, the excess pressure inside the soap bubble is:
\[ \Delta P = \frac{4S}{R} \]

### Final Answer:
The excess pressure inside the soap bubble is \( \frac{4S}{R} \).