Solution:

When a soap bubble is given a negative charge, the radius of the bubble increases. Here's why:

• A soap bubble with charge experiences electrostatic repulsion between the like charges distributed on its surface. This repulsion causes the surface to expand.
• The electrostatic pressure $P$ on the surface of a charged sphere (or bubble) is given by the formula:

$$P = \frac{2 \sigma^2}{\varepsilon_0}$$

where $\sigma$ is the surface charge density, and $\varepsilon_0$ is the permittivity of free space. This pressure acts to push the bubble outward.

• To counteract this, the bubble expands, increasing its radius in response to the electrostatic repulsion.

Thus, when a soap bubble is negatively charged, the repulsion between the charges causes the bubble's radius to increase.