A spherical drop of water carrying a charge of 30 pC has a...

A spherical drop of water carrying a charge of 30 pC has a potential of 500 $\mathrm{V}$ at its surface (with $V=0$ at infinity) (a) What is the radius of the drop? (b) If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop?

A spherical drop of water carrying a charge of 30
pC has a potential of 500 $\mathrm{V}$ at its surface (with $V=0$ at infinity)
(a) What is the radius of the drop? (b) If two such drops of the
same charge and radius combine to form a single spherical drop,
what is the potential at the surface
of the new drop?

Key Concepts

Conservation of Charge

This principle states that the total electric charge in an isolated system remains constant over time, regardless of any physical changes. In cases where multiple charged bodies combine, such as merging droplets, the sum of their individual charges must equal the total charge of the resulting object. This concept is crucial when determining the properties of the new system after coalescence.

Geometric Relationships for Spheres

When dealing with problems involving spherical objects, it is important to recognize how volume scales with the radius. The volume of a sphere is proportional to the cube of its radius (V ? R³), meaning that when two spheres merge, the radius of the resulting sphere is determined by the sum of their volumes using the cube root relationship. This understanding is critical when analyzing how changes in the size of charged spheres affect their physical and electrical properties.

Electric Potential of a Charged Sphere

This concept involves understanding that a charged sphere, acting like a conductor, has an electric potential at its surface determined by its charge and radius. The relationship is given by V = Q/(4???R), which is derived from Coulomb's law. This formula is essential for calculating how the potential depends on the distribution of charge over a spherical surface, under the assumption that all charge resides on the exterior.

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