Conductors, capacitors and dielectrics

At a point of the surface of a conductor in equilibrium the surface charge density is $\sigma =5.0\mu C/{\mathrm{m}}^2$. Compute the magnitude of the electric field at points just outside and state its direction.

Solution available to those who have unlocked the subject.

A conducting sphere of radius $R=15\mathrm{cm}$ is in air, whose dielectric strength is $3.0\cdot 10^{6}V/m$. Compute the maximum charge the sphere can carry without the surrounding air becoming conducting, and the corresponding potential relative to infinity.

Solution available to those who have unlocked the subject.

A neutral conducting spherical shell has outer radius $10\mathrm{cm}$. In the cavity, at an arbitrary position, there is a point charge $q=5.0\mathrm{nC}$. Compute the charge on the inner surface and on the outer surface of the shell, and the magnitude of the field at $20\mathrm{cm}$ from the center of the shell.

Solution available to those who have unlocked the subject.

Compute the plate area of a parallel-plate capacitor in vacuum that has capacitance $C=100\mathrm{pF}$ with the plates at a distance $d=0.40\mathrm{mm}$.

Solution available to those who have unlocked the subject.

An isolated parallel-plate capacitor in vacuum has plates of area $A=0.10{\mathrm{m}}^2$ and carries the charge $Q=0.50\mu \mathrm{C}$. Compute the magnitude of the force with which the plates attract each other.

Solution available to those who have unlocked the subject.

The capacitors $C_1=6.0\mu \mathrm{F}$ and $C_2=3.0\mu \mathrm{F}$ are connected in series, and the series is connected in parallel with $C_3=4.0\mu \mathrm{F}$. The potential difference $\Delta V=30\mathrm{V}$ is applied to the network, initially uncharged. Compute the equivalent capacitance, the charge of each capacitor and the potential differences across $C_1$ and $C_2$.

Solution available to those who have unlocked the subject.

Four identical capacitors are available, each of $10\mu \mathrm{F}$ with maximum voltage $100\mathrm{V}$. State how to connect them to obtain an equivalent capacitor of $10\mu \mathrm{F}$ that withstands $200\mathrm{V}$.

Solution available to those who have unlocked the subject.

A spherical capacitor consists of a conducting sphere of radius $R_1=10\mathrm{cm}$ and a concentric shell of inner radius $R_2=12\mathrm{cm}$, with vacuum in between. Compute the capacitance.

Solution available to those who have unlocked the subject.

A coaxial cable has an inner conductor of radius $a=1.0\mathrm{mm}$ and an outer conductor of inner radius $b=3.5\mathrm{mm}$; the space between the conductors is filled with polyethylene, with ${\epsilon }_r=2.3$. Compute the capacitance per unit length and the capacitance of a $25\mathrm{m}$ length of cable.

Solution available to those who have unlocked the subject.

A parallel-plate capacitor in vacuum has plates of area $A=0.010{\mathrm{m}}^2$ at a distance $d=0.50\mathrm{mm}$ and is charged to $\Delta V=300\mathrm{V}$. Compute the stored energy and the energy density of the field between the plates.

Solution available to those who have unlocked the subject.

A $20\mathrm{pF}$ capacitor in vacuum is charged to $500\mathrm{V}$ and disconnected from the source; then the space between the plates is filled with a dielectric of constant ${\epsilon }_r=5.0$. Compute the final potential difference and the energy stored before and after the insertion.

Solution available to those who have unlocked the subject.

A parallel-plate capacitor has plates of area $A=0.020{\mathrm{m}}^2$ at a distance $d=3.0\mathrm{mm}$. A glass slab of area $A$, thickness $s=2.0\mathrm{mm}$ and relative permittivity ${\epsilon }_r=5.0$ is inserted between the plates, parallel to them. Compute the capacitance.

Solution available to those who have unlocked the subject.

A capacitor $C_1=2.0\mu \mathrm{F}$ is charged to $60\mathrm{V}$ and a capacitor $C_2=3.0\mu \mathrm{F}$ is charged to $20\mathrm{V}$. Both are disconnected from the sources and connected by joining the positive plate of each with the negative plate of the other. Compute the final potential difference and the energy dissipated in the connection.

Solution available to those who have unlocked the subject.