A conductor with an inner cavity, like that shown in Fig. $22.23$c, carries a total charge of $+5.00$ nC. The charge within the cavity, insulated from the conductor, is $-6.00$ nC. How much charge is on (a) the inner surface of the conductor and (b) the outer surface of the conductor?

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?

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 electric flux through a spherical surface just inside the inner surface of the sphere?

An infinitely long cylindrical conductor has radius $r$ and uniform surface charge density $\sigma$. In terms of $\sigma$, what is the magnitude of the electric field produced by the charged cylinder at a distance $r>R$ from its axis? Then, express the result in terms of $\lambda$ and show that the electric field outside the cylinder is the same as if all the charge were on the axis.

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 electric field at a distance of $2.00$ cm from the sphere's center?

An infinitely long cylindrical conductor has radius $r$ and uniform surface charge density $\sigma$. In terms of $\sigma$ and $R$, what is the charge per unit length $\lambda$ for the cylinder?

A very long conducting tube (hollow cylinder) has inner radius $A$ and outer radius $b$. It carries charge per unit length $+α$, where $\alpha$ is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length. Calculate the electric field in terms of $\alpha$ and the distance $r$ from the axis of the tube for (i) ; (ii) ; (iii) $r>b$. Show your results in a graph of $E$ as a function of $R$.