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A conducting sphere is a solid object that can distribute electric charge across its surface evenly. This property arises because the sphere is made from a conductive material, allowing electrons to move freely. When a conducting sphere is charged, the charge resides entirely on the surface. This is due to the repulsion between like charges: electrons spread as far apart as possible, which results in a uniform distribution over the sphere's surface.

The presence of a charge on a conducting sphere influences the electric potential surrounding it. An important characteristic of a conducting sphere is that inside the sphere, the electric field is zero. This means any charge placed inside does not experience a force due to the sphere's surface charge.

• Electric field inside a conducting sphere: zero
• Charge distribution: only on the surface
• Influences electric potential in the surrounding space

Potential difference, often called voltage, is a measure of the work done in moving a unit charge between two points in an electric field. In the context of a conducting sphere and a concentric shell, the potential difference is the work needed to move charge from the sphere's surface to the shell's surface. This is crucial in understanding how charges affect one another at a distance.

In our specific problem, the potential difference between the surface of the conducting sphere and the hollow spherical shell initially depends only on the charge of the sphere, given the shell begins with no charge. When this changes and the shell gains a charge of \( -3Q \), the potential difference between these two surfaces changes as well. Mathematically, this can be expressed as \(V = k\frac{Q}{R_1} - k\frac{Q}{R_2}\), where \(k\) is Coulomb's constant, and \(R_1\) and \(R_2\) are radii of the inner and outer spheres, respectively.

• Definition: Work to move charge between two points
• Depends on charge magnitude and configuration
• Influences by adding/removing charge

Coulomb's Law describes the force between two charged objects. It states that the force \(F\) between two point charges is directly proportional to the product of the charges (\(q_1\) and \(q_2\)) and inversely proportional to the square of the distance \(r\) between them. The equation is given by \(F = k\frac{q_1 q_2}{r^2}\), where \(k\) is the electrostatic constant.

This law is fundamental in calculating the interactions between charged objects, like in our exercise involving a conducting sphere and a spherical shell. Coulomb's Law helps determine the electric potential difference because the potential difference is derived from the electric field, which originates from these forces. Understanding how charges interact, distribute themselves, and influence potential is grounded in this foundational principle.

• Force depends on product of charges
• Force is inversely related to distance squared
• Key law in electrostatics