Two long parallel plates are separated by a distance of 15.0 cm. The bottom plate is kept at a potential of −250 V and the top at

$$+ 250 \mathrm { V }$$

. A charge of

$$- 2.00 \mu \mathrm { C }$$

is placed at a point 3.00 cm from the bottom plate. a. Find the electric potential energy of the charge. The charge is then moved vertically up to a point 3.00 cm from the top plate. b. What is the electrical potential energy of the charge now? c. How much work was done on the charge?

In the example earlier, was analyzed a parallel-plate capacitor (plate area $L \times L$ with $L=0.10 \mu \mathrm{m}$ and a plate separation of $10 \mathrm{~nm}$ ) as might be found in an integrated circuit (RAM chip), but we omitted the dielectric that would usually be found between the plates. This dielectric is composed of $\mathrm{SiO}_2$ and has a dielectric constant close to that of glass. What is the capacitance of the RAM capacitor in the example given when it is filled with $\mathrm{SiO}_2$ ?

Helium at 3 atm and $73^{\circ} \mathrm{C}$ flows across a $35$-$\mathrm{cm}$-square plate that is maintained at a surface temperature of $113^{\circ} \mathrm{C}$. The free-stream velocity is $50 \mathrm{~m} / \mathrm{s}$. Determine the convection heat lost by the plate.

Compare and contrast the following: a) growth plate (epiphyseal plate) and cartilaginous line (epiphyseal line) b) photographic superimposition and craniofacial reconstruction c) the teeth found in the skeletal remains of a 4-year old child and the teeth found in the skeletal remains of an 8-year old child.

A double plate-glass window is constructed with a 1.25-cm air space. The plate dimensions are 1.2 by 1.8 m. Determine the free-convection heat-transfer rate through the air space for a temperature difference of $30^{\circ} \mathrm{C}$ and $T_1=20^{\circ} \mathrm{C}$.

The liquid confined between two plates is assumed to have a linear velocity distribution as shown. If the pressure at the top surface of the bottom plate is $600 \mathrm{~N} / \mathrm{m}^2$, find the pressure at the bottom surface of the top plate, Take $\rho=1.2\ \mathrm{Mg} / \mathrm{m}^3$.

A flat metal plate lying in the $x y$ plane is heated in such a way that the temperature at the point $(x, y)$ is $T^{\circ} \mathrm{C}$, where

$$T(x, y)=10 y e^{-x y}$$

Find the average temperature over a rectangular portion of the plate for which $0 \leq x \leq 2$ and $0 \leq y \leq 1$.

Two equal but opposite charges are placed on the $x$-axis as shown. The positive charge is placed to the left of the origin, and the negative charge is placed to the right. Copy the figure on a piece of paper. Sketch the direction of the net electric field at points $A$ and $B$.

Carbon dioxide and hydrogen as ideal gases at 1 atm and $-20^\circ C$ flow in parallel over a flat plate. The flow velocity of each gas is 1 m/s and the surface temperature of the 3-m-long plate is maintained at $20^\circ C.$ Using the EES (or other) software, evaluate the local Reynolds number, the local Nusselt number, and the local convection heat transfer coefficient along the plate for each gas. By varying the location along the plate for $0.2 \leq x \leq 3 \mathrm{m},$ plot the local Reynolds number, the local Nusselt number, and the local convection heat transfer coefficient for each gas as functions of x. Discuss which gas has higher local Nusselt number and which gas has higher convection heat transfer coefficient along the plate. Assume flow is laminar but make sure to verify this assumption.

The mass of the suspended object is $6 \mathrm{~kg}$. The structure is supported at $B$ by the normal and friction forces exerted on the plate by the wall. Neglect the weights of the bars. (a) What is the magnitude of the friction force exerted on the plate at $B$ ? (b) What is the minimum coefficient of static friction at $B$ necessary for the structure to remain in equilibrium?

An uncharged capacitor is connected to the terminals of a 3.0 V battery, and $6.0 \mu \mathrm { C }$ flows to the positive plate. The 3.0 V battery is then disconnected and replaced with a 5.0 V battery, with the positive and negative terminals connected in the same manner as before. How much additional charge flows to the positive plate?

Careful measurements made during the impact of the 200-g metal cylinder with the spring-loaded plate reveal a semielliptical relation between the contact force $F$ and the time $t$ of impact as shown. Determine the rebound velocity $v$ of the cylinder if it strikes the plate with a velocity of $6 \mathrm{~m} / \mathrm{s}$.

For the hypothetical boundary layer on the flat plate shown in the given figure, what is the shear stress on the plate at the downstream end (point A)? Here $\rho=1.2 \mathrm{~kg} / \mathrm{m}^3$ and $\mu=1.8 \times 10^{-5} \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$.

An air-filled parallel-plate capacitor with plate separation d and plate area A is connected to a battery that applies a voltage $V_{0}$ between plates. With the battery left connected, the plates are moved apart to a distance of 10d. Determine by what factor each of the following quantities changes: (a) $V_{0} ;(b) C ;(c) E ;(d) D ;(e) Q ;(f) \rho_{S} ;(g) W_{E}.$ Repeat the exercise for the case in which the battery is disconnected before the plates are separated.