Una carga puntual de q=5,0 ×10^-8 C se coloca en el centro de una capa conductora esférica sin c

Step 1: Determine the potential due to the point charge at the center of the spherical conductor

Una carga puntual de q=5,0 ×10^-8 C se coloca en el centro...

Una carga puntual de $q=5,0 \times 10^{-8} \mathrm{C}$ se coloca en el centro de una capa conductora esférica sin carga de radio interior $6,0 \mathrm{~cm}$ y radio exterior $9,0 \mathrm{~cm}$. Encuentre el potencial eléctrico en (a) $r=4,0 \mathrm{~cm}$, (b) $r=8,0 \mathrm{~cm}$, (c) $r=12,0 \mathrm{~cm}$.

Key Concepts

Superposition Principle in Electrostatics

The principle states that the total electric potential at any point is the algebraic sum of the potentials due to each individual charge or charge distribution. This concept is crucial when combining the effects of a point charge with those of induced charges on the surfaces of a conductor.

Electrostatic Properties of Conductors

In conductors at electrostatic equilibrium, the electric field inside is zero, which means the potential is constant throughout the conductor. This property ensures that any induced charges on a conductor’s surfaces arrange themselves such that the potential on both the inner and outer surfaces remains continuous and constant.

Electric Potential of a Point Charge

This concept explains that the electric potential produced by a point charge is determined by the formula V = kq/r, where k is Coulomb's constant, q is the charge, and r is the distance from the charge. It is fundamental in understanding how potentials vary with distance in radially symmetric fields.

Gauss's Law in Spherical Symmetry

Gauss’s law is used to relate the electric flux through a closed surface with the charge enclosed by that surface. In spherical systems, symmetry simplifies the application of Gauss’s law, allowing one to determine the electric field and subsequently calculate the potential by integration.

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