A $1-\mu \mathrm{C}$ point charge is embedded in the center of a solid Pyrex sphere of radius $R=10 \mathrm{~cm}$. (a) Calculate the electric field strength $E$ just beneath the surface of the sphere. (b) Assuming that there are no other free charges, calculate the strength of the electric field just outside the surface of the sphere. (c) What is the induced surface charge density $\sigma_{\text {ind }}$ on the surface of the Pyrex sphere?

A block of linearly elastic material $(E, \nu)$ is compressed between two rigid, perfectly smooth surfaces by an applied stress $\sigma_x=-\sigma_0$, as depicted in Fig. . The only other nonzero stress is the stress $\sigma_y$ induced by the restraining surfaces at $y=0$ and $y=b$. (a) Determine the value of the restraining stress $\sigma_y$. (b) Determine $\Delta a$, the change in the $x$ dimension of the block. (c) Determine the change $\Delta t$ in the thickness $t$ in the $z$ direction.

A short coil with radius $R=10.0 \mathrm{~cm}$ contains $N=30.0$ turns and surrounds a long solenoid with radius $r=8.00 \mathrm{~cm}$ containing $n=60$ turns per centimeter. The current in the short coil is increased at a constant rate from zero to $i=2.00 \mathrm{~A}$ in a time of $t=12.0 \mathrm{~s}$. Calculate the induced potential difference in the long solenoid while the current is increasing in the short coil.

A voltage regulator is to have a nominal output voltage of $10 \mathrm{~V}$. The specified Zener diode has a rating of $1 \mathrm{~W}$, has a $10 \mathrm{~V}$ drop at $I_Z=25 \mathrm{~mA}$, and has a Zener resistance of $r_z=5 \Omega$. The input power supply has a nominal value of $V_{P S}=20 \mathrm{~V}$ and can vary by $\pm 25$ percent. The output load current is to vary between $I_L=0$ and $20 \mathrm{~mA}$. (a) If the minimum Zener current is to be $I_Z=5 \mathrm{~mA}$, determine the required $R_j$. (b) Determine the maximum variation in output voltage. (c) Determine the percent regulation.

A steam engine based on a turbine is shown in figure. The boiler tank has a volume of $100 \mathrm{~L}$ and initially contains saturated liquid with a very small amount of vapor at $100 \mathrm{kPa}$. Heat is now added by the burner. The pressure regulator, which keeps the pressure constant, does not open before the boiler pressure reaches $700 \mathrm{kPa}$. The saturated vapor enters the turbine at $700 \mathrm{kPa}$ and is discharged to the atmosphere as saturated vapor at $100 \mathrm{kPa}$. The burner is turned off when no more liquid is present in the boiler. Find the total turbine work and the total heat transfer to the boiler for this process.

A circular conducting coil with radius 3.40 cm is placed in a uniform magnetic field of 0.880 T with the plane of the coil perpendicular to the magnetic field. The coil is rotated $180 ^ { \circ }$ about the axis in 0.222 s. (a) What is the average induced emf in the coil during this rotation? (b) If the coil is made of copper with a diameter of 0.900 mm, what is the average current that flows through the coil during the rotation?

In an elegant experiment on the nature of receptor tyrosine kinase signaling, a gene was synthesized that encoded a chimeric receptor—the extracellular part came from the insulin receptor, and the membrane spanning and cytoplasmic parts came from the EGF receptor. The striking result was that the binding of insulin induced tyrosine kinase activity, as evidenced by rapid autophosphorylation. What does this result tell you about the signaling mechanisms of the EGF and insulin receptors?

Calculate the potential difference induced between the tips of the wings of a Boelng 747-400 with a wingspan of $64.67 \mathrm{~m}$ when it is in level flight at a speed of $913 \mathrm{~km} / \mathrm{h}$. Assume that the magnttude of the downward component of the Farth's magnetic field $15 B=5.00 \cdot 10^{-5} \mathrm{~T}$. a) $0.820 \mathrm{~V}$ b) $2.95 \mathrm{~V}$ c) $10.4 \mathrm{~V}$ d) $30.1 \mathrm{~V}$ e) $225 \mathrm{~V}$

A 50-turn rectangular coil with dimensions $0.15 \mathrm { m } \times 0.40 \mathrm { m }$ rotates in a uniform magnetic field of magnitude 0.75 T at 3600 rev/min. (a) Determine the emf induced in the coil as a function of time. (b) If the coil is connected to a $1000 - \Omega$ resistor, what is the power as a function of time required to keep the coil turning at 3600 rpm? (c) Answer part (b) if the coil is connected to a $2000 - \Omega$ resistor.

The current in a very long, tightly wound solenoid with radius $a$ and $n$ turns per unit length varies over time according to the equation $i(t)=C t^2$, where the current $i$ is in amps and the time $t$ is in seconds, and $C$ is a constant with appropriate units. Concentric with the solenoid is a conducting ring of radius $r$, as shown in the figure. b) Write an expression for the magnitude of the electric field induced at an arbitrary point on the ring.

Consider the truss in Prob. . Suppose that member (3) was originally fabricated $0.05$ in. too short (i.e., $\bar{\delta}_3=0.05 \mathrm{in}$.) so that it had to be temporarily stretched enough to insert the pin at $A$. (a) If $P=0$, what displacements $u_A$ and $v_A$ will result when the truss is forcefully assembled as described above? (b) What "initial stresses" $-\sigma_1$, $\sigma_2$, and $\sigma_3$-will be induced in the members when the truss is forcefully assembled?

At a place directly below a thundercloud, the induced electric charge on the surface of the Earth is $+1.0 \times 10^{-7}$ coulomb per square meter of surface. How many singly charged positive ions per square meter does this represent? The number of atoms on the surface of a solid is typically $2.0 \times 10^{19}$ per square meter. What fraction of these atoms must be ions to account for the above electric charge?

Design a voltage regulator circuit so that $V_L=7.5 \mathrm{~V}$. The Zener diode voltage is $V_Z=7.5 \mathrm{~V}$ at $I_Z=10 \mathrm{~mA}$. The incremental diode resistance is $r_z=12 \Omega$. The nominal supply voltage is $V_l=12 \mathrm{~V}$ and the nominal load resistance is $R_L=1 \mathrm{k} \Omega$. (a) Determine $R_i$. (b) If $V_I$ varies by $\pm 10$ percent, calculate the source regulation. What is the variation in output voltage? (c) If $R_L$ varies over the range of $1 \mathrm{k} \Omega \leq R_L \leq \infty$, what is the variation in output voltage? Determine the load regulation.

A satellite, orbiting the earth at the equator at an altitude of $400 \mathrm{~km}$, has an antenna that can be modeled as a $2.0 \mathrm{~m}$ long rod. The antenna is oriented perpendicular to the earth's surface. At the equator, the earth's magnetic field is essentially horizontal and has a value of $8.0 \times 10^{-5} \mathrm{~T}$; ignore any changes in $B$ with altitude. Assuming the orbit is circular, determine the induced emf between the tips of the antenna.