Figure E$24.14$ shows a system of four capacitors, where the potential difference across ab is $50.0$ V. How much charge is stored in each of the $10.0$-$\mu$F and the $9.0$-$\mu$F capacitors?

For the system of capacitors shown in Fig. E$24.16$, find the equivalent capacitance between $b$ and $c$.

In Fig. E$24.20$, $C_1=6.00$ $\mu$F, $C_2=3.00$ $\mu$F, and $C_3=5.00$ $\mu$F. The capacitor network is connected to an applied potential $V_{ab}$.

(a) After the charges on the capacitors have reached their final values, the charge on $C_2$ is $30.0$ mC. What are the charges on capacitors $C_1$ and $C_3$?

(b) What is the applied voltage $V_{ab}$?

A $5.80$-$\mu$F, parallel-plate, air capacitor has a plate separation of $5.00$ mm and is charged to a potential difference of $400$ V. Calculate the energy density in the region between the plates, in units of J/m³.

A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is $10.0$ pC. The inner cylinder has radius $0.50$ mm, the outer one has radius $5.00$ mm, and the length of each cylinder is $18.0$ cm.

(a) What is the capacitance?

(b) What applied potential difference is necessary to produce these charges on the cylinders?

Figure E$24.14$ shows a system of four capacitors, where the potential difference across ab is $50.0$ V. How much charge is stored by this combination of capacitors?

A spherical capacitor contains a charge of $3.30$ nC when connected to a potential difference of $220$ V. If its plates are separated by vacuum and the inner radius of the outer shell is $4.00$ cm, calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.