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 are (a) the volume charge density for the sphere?

A cube has sides equal to $4.0\mathrm{cm}$. The net flux through the cube is $12\mathrm{N}·{\mathrm{m}}^2/\mathrm{C}$ outward. Is the net charge in the cube positive, negative or zero?

An electric field with strength $3500\mathrm{N}/\mathrm{C}$ exists just outside a face of a large block of aluminum. If the electric field points towards the block, what is the surface charge density on the face of the block?

A sphere of radius $4.0\mathrm{cm}$ has a charge of $23\mathrm{nC}$ evenly distributed throughout the sphere. What is the electric field strength $1.0\mathrm{cm}$ from the center of the sphere?

An insulating sphere of radius $4.0\mathrm{cm}$ is in the center of a conducting spherical shell with inner radius of $5.0\mathrm{cm}$ and outer radius of $7.0\mathrm{cm}$. The insulating sphere has a charge of $-34\mathrm{nC}$ and the conducting spherical shell has a net charge of $42\mathrm{nC}$. What is the total charge on the inner surface of the conducting spherical shell?

A very long insulating cylinder has radius $4.7\mathrm{cm}$. Every $3.0\mathrm{m}$ length of the cylinder contains a charge of $86\mathrm{nC}$ evenly distributed throughout. What is the strength of the electric field $3.0\mathrm{cm}$ from the axis of the cylinder?

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 12.0 cm, giving it a charge of −49.0 μ C. Find the electric field (b) just outside the paint layer;

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 12.0 cm, giving it a charge of −49.0 μ C. Find the electric field (a) just inside the paint layer;

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 7.4×10−15 m. (c) 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 7.4×10−15 m. (b) What magnitude of electric field does it produce at the distance of the electrons, which is about 1.0×10−10 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 7.4×10−15 m. (a) 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 −3.63×1016 N·m2/C at the planet's surface. Calculate:(c) 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 −3.63×1016 N·m2/C at the planet's surface. Calculate: (b) the electric field at the planet's surface (refer to the astronomical data inside the back cover);