Air “breaks down” when the electric field strength reaches $3.0 \times 10^{6} \mathrm{N} / \mathrm{C}$, causing a spark. A parallel-plate capacitor is made from two $4.0 \mathrm{cm} \times 4.0 \mathrm{cm}$ electrodes. How many electrons must be transferred from one electrode to the other to create a spark between the electrodes?

You witnessed a bank robbery last night! Look at the pictures below that illustrate what happened, then write complete sentences to answer the police officer's questions that follow. Use the preterite forms of the verbs ser and/or ir in each sentence. ¿Adónde fuiste tú? _____

A parallel-plate capacitor is formed from two 6.0-cm-diameter electrodes spaced 2.0 mm apart. The electric field strength inside the capacitor is $1.0 \times 10^{6} \mathrm{N} / \mathrm{C}$. What is the charge (in nC) on each electrode?

A small glass bead has been charged to $+ 20 \mathrm { nC }$. What are the magnitude and direction of the acceleration of (a) a proton and (b) and (b) an electron that is 1.0 cm from the center of the bead?

A bumblebee can sense electric fields as the fields BID bend hairs on its body. Bumblebees have been conclusively shown to detect an electric field of $60 \mathrm{~N} / \mathrm{C}$. Could a bumblebee use this sense to detect the presence of another nearby bumblebee? Suppose a bumblebee has a charge of $24 \mathrm{pC}$. How far away could another bumblebee detect its presence?

A small plastic sphere with a charge of $- 5.0 \mathrm { nC }$ is near another small plastic sphere with a charge of $- 12 \mathrm { nC }$. If the spheres repel one another with a force of magnitude $8.2 \times 10 ^ { - 4 } \mathrm { N }$, what is the distance between the spheres?

Find a vector perpendicular to both $i − 3j + 2k$ and $5i − j − 4k.$

Test the following series for convergence or divergence. Decide for yourself which test is easiest to use, but don’t forget the preliminary test. Use the facts stated above when they apply. $\sum_{n=2}^{\infty} \frac{(-1)^{n}}{n^{2}-n}$

Two 10-cm-diameter electrodes 0.50 cm apart form a parallel-plate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. After a long time, the capacitor is disconnected from the battery but is not discharged. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes a. Right after the battery is disconnected? b. After insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apart? c. After the original electrodes (not the modified electrodes of part b) are expanded until they a re 20 cm in diameter?

Two 10.0-cm-diameter electrodes 0.50 cm apart form a parallel-plate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes a. While the capacitor is attached to the battery? b. After insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apart? The electrodes remain connected to the battery during this process.

Two point charges are located at two corners of a rectangle, as shown in the figure. a) What is the electric potential at point $A$ ? b) What is the potential difference between points $A$ and $B$ ?

Write and solve the Euler equations to make the following integrals stationary. $\int_{x_{1}}^{x_{2}} x d s$

Find (A) $f^{\prime}(x),(B)$ the partition numbers for $f^{\prime}$, and (C) the critical numbers of f. f(x)=|x|

In ideal flow, a liquid of density $850 \mathrm{kg} / \mathrm{m}^{3}$ moves from a horizontal tube of radius 1.00 cm into a second horizontal tube of radius 0.500 cm at the same elevation as the first tube. The pressure differs by $\Delta P$ between the liquid in one tube and the liquid in the second tube. (a) Find the volume flow rate as a function of $\Delta P$. Evaluate the volume flow rate for (b) $\Delta P=6.00 \mathrm{kPa}$ and (c) $\Delta P=12.0 \mathrm{kPa}$.