24. Electric Force & Field; Gauss' Law

Charge $q$ is distributed uniformly throughout the volume of an insulating sphere of radius $R=4.00$ cm. At a distance of $r=8.00$ cm from the center of the sphere, the electric field due to the charge distribution has magnitude $E=940$ N/C. What is the volume charge density for the sphere?

Rank the flux through surfaces A, B and C in the figure below from greatest to smallest.

A spherical, thin conducting shell of radius 8cm has a charge of –6C. If a 4C charge were placed at the center of the shell, what is the electric field 4 cm from the center? At 12 cm?

The nuclei of large atoms, such as uranium, with $92$ protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4\times10^{-15}$ m. The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?

The nuclei of large atoms, such as uranium, with $92$ protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4\times {10}^{-15}$ m. What is the electric field this nucleus produces just outside its surface?

Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of $-3.63\times10^{16}$ Nm²/C at the planet's surface. Calculate the charge density on Mars, assuming all the charge is uniformly distributed over the planet's surface.

Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of $-3.63\times10^{16}$ Nm²/C at the planet's surface. Calculate the electric field at the planet's surface (refer to the astronomical data inside the back cover).

Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of $-3.63\times {10}^{16}$ Nm²/C at the planet's surface. Calculate the total electric charge on the planet.

A very long uniform line of charge has charge per unit length $4.80$ $\mu$C/m and lies along the $x$-axis. A second long uniform line of charge has charge per unit length $-2.40$ $\mu$C/m and is parallel to the $x$-axis at $y=0.400$ m. What is the net electric field (magnitude and direction) at the following points on the $y$-axis: (a) $y=0.200$ m and (b) $y=0.600$ m?

A hollow, conducting sphere with an outer radius of $0.250$ m and an inner radius of $0.200$ m has a uniform surface charge density of $+6.37\times10^{-6}$ C/m². A charge of $−0.500$ $\mu$C is now introduced at the center of the cavity inside the sphere. What is the electric flux through a spherical surface just inside the inner surface of the sphere?