A solenoid $95.6 \mathrm{~cm}$ long has a radius of $1.90 \mathrm{~cm}$, a winding of 1230 turns, and carries a current of $3.58 \mathrm{~A}$. Calculate the strength of the magnetic field inside the solenoid.

A steady current is set up in a cubical network of resistive wires, as in given figure. Use symmetry arguments to show that the magnetic field at the center of the cube is zero.

The magnetic field at the center of a circular current loop has the value $B=\mu_0 i / 2 R$; However. the electric field at the center of a ring of charge is zero. Why this difference?

Two long solenoids are nested on the same axis. They carry identical currents but in opposite directions. If there is no magnetic field inside the inner solenoid, what can you say about $n$, the number of turns per unit length, for the two solenoids? Which one, if either, has the larger value?

A long, straight wire carries a constant current $i$. What does Ampere's law require for $(a)$ a loop that encloses the wire but is not circular, (b) a loop that does not enclose the wire, and (c) a loop that encloses the wire but does not all lie in one plane?

At a location in the Philippines, the Earth's magnetic field has a value of $39.0 \mu \mathrm{T}$ and is horizontal and due north. The net field is zero $8.13 \mathrm{~cm}$ above a long, straight, horizontal wire that carries a steady current. (a) Calculate the current and (b) find its direction.

A surveyor is using a magnetic compass $6.3 \mathrm{~m}$ below a power line in which there is a steady current of $120 \mathrm{~A}$. Will this interfere seriously with the compass reading? The horizontal component of Earth's magnetic field at the site is $210 \mu \mathrm{T}$.

An idealized schematic of an "electromagnetic rail gun, (as shown in figure) " which is designed to fire projectiles at speeds up to $10 \mathrm{~km} / \mathrm{s}$. The projectile $P$ sits between and in contact with two parallel rails along which it can slide. A generator G provides a current that flows up one rail, across the projectile, and back down the other rail. (a) Let $w$ be the distance between the rails, $r$ the radius of the rails (presumed circular), and $i$ the current. Show that the force on the projectile is to the right and given approximately by

$$F=\frac{1}{2}\left(\frac{i^2 \mu_0}{\pi}\right) \ln \left(\frac{n+r}{r}\right) .$$

The $25-\mathrm{kV}$ electron gun in a TV tube fires an electron beam $0.22 \mathrm{~mm}$ in diameter at the screen, $5.6 \times 10^{14}$ electrons arriving each second. Calculate the magnetic field produced by the beam at a point $1.5 \mathrm{~mm}$ from the axis of the beam.

A 10-gauge bare copper wire (2.6 mm in diameter) can carry a current of 50 A without overheating. For this current, what is the magnitude of the magnetic field at the surface of the wire?

Five long. parallel wires in the $x y$ plane. Each wire carries a current $i=3.22 \mathrm{~A}$ in the positive $x$ direction. The separation between adjacent wires is $a=8.30 \mathrm{~cm}$. Find the magnetic force per meter, magnitude and direction, exerted on each of these five wires.

In a mass spectrometer used for commercial purposes, uranium ions of mass $238 \mathrm{u}$ and charge $+2 e$ are separated from related species. The ions are first accelerated through a potential difference of $105 \mathrm{kV}$ and then pass into a magnetic field, where they travel a $180^{\circ}$ arc of radius $97.3 \mathrm{~cm}$. They are then collected in a cup after passing through a slit of width $1.20 \mathrm{~mm}$ and a height of $1.14 \mathrm{~cm}$. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is designed to separate out $90.0 \mathrm{mg}$ of material per hour, calculate $(b)$ the current of the desired ions in the machine and $(c)$ the internal energy dissipated in the cup in $1.00 \mathrm{~h}$.

The given Figure shows an arrangement used to measure the masses of ions. An ion of mass $m$ and charge $+q$ is produced essentially at rest in source S, a chamber in which a gas dis. charge is taking place. The ion is accelerated by potential dif. ference $\Delta V$ and allowed to enter a magnetic field $\overrightarrow{\mathrm{B}}$. In the field it moves in a semicircle, striking a photographic plate at distance $x$ from the entry slit. Show that the ion mass $m$ is given by

$$m=\frac{B^2 q}{8 \Delta V} x^2$$

Bainbridge's mass spectrometer, separates ions having the same velocity. The ions, after entering through slits $S_1$ and $S_2$, pass through a velocity selector composed of an electric field produced by the charged plates P and $\mathbf{P}^{\prime}$, and a magnetic field $\overrightarrow{\mathbf{B}}$ perpendicular to the electric field and the ion path. Those ions that pass undeviated through the crossed $\overrightarrow{\mathbf{E}}$ and $\overrightarrow{\mathbf{B}}$ fields enter into a region where a second magnetic field $\vec{B}^{\prime}$ exists, and are bent into circular paths. A photographic plate registers their arrival. Show thal $q / m=E / r B B^{\prime}$, where $r$ is the radius of the circular orbit.