A parallel-plate capacitor is charged by being connected to a battery and is kept connected to the battery. The separation between the plates is then doubled. How does the electric field change? The charge on the plates? The total energy? Explain.

The charged plates of a capacitor attract each other, so to pull the plates farther apart requires work by some external force. What becomes of the energy added by this work? Explain.

Suppose several different parallel-plate capacitors are charged up by a constant-voltage source. Thinking of the actual movement and position of the charges on an atomic level, why does it make sense that the capacitances are proportional to the surface areas of the plates? Why does it make sense that the capacitances are inversely proportional to the distance between the plates?

Is dielectric strength the same thing as dielectric constant? Explain any differences between the two quantities. Is there a simple relationship between dielectric strength and dielectric constant (see Table)? " $$ \begin{matrix} \text{Dielectric Constant and Dielectric Strength of Some Insulating Materials}\\ \end{matrix} $$ " " $$ \begin{matrix} & \text{Dielectric} & \text{Dielectric Strength,}\\ \text{Material} & \text{Constant, K} & \text{E_m (V/m)}\\ \text{Polycarbonate} & \text{2.8} & \mathrm{3 \times 10^{7}}\\ \mathrm{Polyester} & \text{3.3} & \mathrm{6 \times 10^{7}}\\ \mathrm{Polypropylene} & \text{2.2} & \mathrm{7 \times 10^{7}}\\ \text{Polystyrene} & \text{2.6} & \mathrm{2 \times 10^{7}}\\ \text{Pyrex glass} & \text{4.7} & \mathrm{1 \times 10^{7}}\\ \end{matrix} $$ "

If $\vec{E}$ is zero everywhere along a certain path that leads from point A to point B, what is the potential difference between those two points? Does this mean that $\vec{E}$ is zero everywhere along any path from A to B? Explain.

A state has registered 8 million automobiles. To simplify the license plate system, a state employee suggests that each plate display only two letters followed by three digits. Will this system create enough different license plates for all the vehicles registered?

The plates of a parallel-plate capacitor have constant charges of +Q and -Q. Do the following quantities increase, decrease, or remain the same as the separation of the plates is increased? (a) the electric field between the plates; (b) the potential difference between the plates ; (c) the capacitance; (d) the energy stored in the capacitor.

A parallel-plate capacitor is connected to a battery that maintains a constant potential difference $V$ between the plates. If the plates of the capacitor are pulled farther apart, does the the energy stored in the capacitor increase, decrease, or remain the same

Suppose two plates lie in parallel horizontal planes, one plate in the xy plane at z = 0 and the other plate in the plane that is parallel to the xy plane at z = 10 mm. Between the plates is a constant electric field directed vertically upward (that is, in the positive z direction). A proton and an electron are launched in the positive x direction with the same initial velocity from position (0, 0, 5.0 mm). If the proton strikes a plate at (200 mm, 0, 10 mm), where does the electron strike?

A $0.200$-A current is charging a capacitor that has circular plates $10.0 \mathrm{~cm}$ in radius. If the plate separation is $4.00 \mathrm{~mm}$,
(a) what is the time rate of increase of electric field between the plates?

The electric potential V in the space between two flat parallel plates 1 and 2 is given (in volts) by V = 1500x$^2$, where x(in meters) is the perpendicular distance from plate 1. At x = 1.3 cm, what is the field directed toward or away from plate 1?

Extend the steady flow between a fixed lower plate and a moving upper plate, from Fig. 1.7 to the case of two immiscible liquids between the plates, as in Fig. P1.57. (a) Draw the expected no-slip velocity distribution $u(y)$ between the plates. $(b)$ Derive an analytic expression for the velocity $U$ at the interface between the two liquid layers. (c) What can be the result of $(b)$ if the viscosities and layer thicknesses are equal?

Calculate the effective value of g, the acceleration of gravity, at 3200 km. above the Earth's surface.

Two 3.00 cm x 3.00 cm plates that form a parallel-plate capacitor are charged to ±0.708 nC. What is the electric field strength inside the capacitor if the spacing between the plates is 1.50 mm?