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?

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 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?

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. Calculate the strength of the electric field just outside the sphere?

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 $+6.37\times {10}^{-6}$ C/m². A charge of $-0.500$ $\mu$C is now introduced at the center of the cavity inside the sphere. What is the new charge density on the outside of the sphere?

You measure an electric field of $1.25\times {10}^6$ N/C at a distance of $0.150$ m from a point charge. There is no other source of electric field in the region other than this point charge.

(a) What is the electric flux through the surface of a sphere that has this charge at its center and that has radius $0.150$ m?

(b) What is the magnitude of this charge?