Examen de Física II URV 2022 · Juny

System setup

A point charge of $-1\text{ nC}$ is located at the center of a conductive spherical shell in electrostatic equilibrium, having inner radius $r_1 = 2\text{ cm}$ and outer radius $r_2 = 4\text{ cm}$. The shell has a net charge of $+3\text{ nC}$.

Assume the permittivity of vacuum to be $\varepsilon_0 = 9 \times 10^{-12}\text{ C}^2/(\text{N}\cdot\text{m}^2)$.

a.

The surface charge density on the exterior surface of the shell.

b.

The electrostatic field in the region between the central point charge and the shell ($0 < r < r_1$). Express the magnitude or radial component as a function of distance $r$ (in meters).

V/m

System setup

A point charge of $-1\text{ nC}$ is located at the center of a conductive spherical shell in electrostatic equilibrium, having inner radius $r_1 = 2\text{ cm}$ and outer radius $r_2 = 4\text{ cm}$. The shell has a net charge of $+3\text{ nC}$.

Assume the permittivity of vacuum to be $\varepsilon_0 = 9 \times 10^{-12}\text{ C}^2/(\text{N}\cdot\text{m}^2)$.

c.

The electric potential on both the internal and external surfaces of the shell.

d.

The electric field and electric potential at a distance of $5\text{ cm}$ from the central charge.

Surface elements of conductors in electrostatic equilibrium connected by a tube of electric field lines (known as corresponding elements) carry related charges. State the relationship between these charges and provide a proof for your statement.

Question 2 (5 points). DC circuit with capacitor and batteries

Given the electrical circuit shown below:

Calculate:

a.

The potential difference across the terminals of the $4\text{ V}$ battery ($V_{AB}$):

b.

The charge stored on the capacitor $C_1$: