A motor has an armature resistance of 3.75 $\Omega$. If it draws 9.20 A when running at full speed and connected to a $120$-$\mathrm{V}$ line, how large is the counter emf?

Gold is a dense metal, with a density of $1.93\times 10^{4} \mathrm{~ kg/m^{3}}$ at T =300 K. (a) If gold has exactly one conduction electron per atom, what is its Fermi energy? Compare your result with the measured value. (b) If the electrons in gold were treated as a classical ideal gas, what would be their mean thermal energy (also at 300 K)? Explain the large discrepancy between your answers in (a) and (b).

If you are given a fixed length of wire, how would you shape it to obtain the greatest self-inductance? The least?

A 450-loop circular armature coil with a diameter of 10.0 cm rotates at $60$ rev/s in a uniform magnetic field of strength $0.75 ~\mathrm{T}$. What is the rms voltage output of the generator? What would you do to the rotation frequency in order to double the rms voltage output?

How would you arrange two flat circular coils so that their mutual inductance was (a) greatest, (b) least (without separating them by a great distance)?

A superconducting magnet carries a $100 \mathrm{~A}$ current through a $0.50$-mm-diameter superconducting wire that is wound into a coil. a. What is the current density in the wire? b. How much charge flows through the wire in 15 minutes?

A simple generator bas a 720-loop square coil 21.0 cm on a side. How fast must it turn in a 0.650-$\mathrm{T}$ field to produce a $120$-$\mathrm{V}$ peak output?

Figure Mentioned is an edge view of three charged metal electrodes. Draw a graph of (a) $E_y$ versus $x$ and (b) $V$ versus $x$ over the region $0 \leq x \leq 3 \mathrm{~cm}$.

A transformer designed for a 120-V ac input will often "burn out" if connected to a 120-V de source. Explain. [Hint: the resistance of the primary coil is usually very low.]

Show that the rms output of an ac generator is $V_{rms} = NAB\omega/\sqrt{2}$.

One $1.0 \mathrm{~g}$ bead is charged to $+10 \mathrm{nC}$, a second to $-10 \mathrm{nC}$. They rotate about their common center of mass at $150 \mathrm{rpm}$. What is the distance between the beads?

The metal sphere in Figure mentioned hangs by a thread. When the north pole of a bar magnet is brought near, the sphere is strongly attracted to the magnet. Then the magnet is reversed and its south pole is brought near the sphere. How does the sphere respond? Explain.

The primary of a transformer on a telephone pole has a resistance of 0.10 $\Omega$ and the input voltage is $2400 ~\mathrm{V}$ ac. Can you estimate the current that will flow? Will it be $24,000 ~\mathrm{A}?$ Explain.

A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball $(r \leq R) \text { is } E(r)=r^{4} E_{\max } / R^{4}$. a. What is $E_{\max }$ in terms of Q and R? b. Find an expression for the volume charge density $\rho(r)$ inside the ball as a function of r. Verify that your charge density gives the total charge Q when integrated over the volume of the ball.