A proton moves along the x-axis with vₓ = 1.0 x 10⁷ m/s. As it passes the origin, what are the strength and direction of the magnetic field at the (x, y, z) positions (a) (1 cm, 0 cm, 0 cm), (b) (0 cm, 1 cm, 0 cm), and (c) (0 cm, -2 cm, 0 cm)?

What is the magnetic field at the position of the dot in FIGURE EX29.6? Give your answer as a vector.

The element niobium, which is a metal, is a superconductor (i.e., no electrical resistance) at temperatures below 9 K. However, the superconductivity is destroyed if the magnetic field at the surface of the metal reaches or exceeds 0.10 T. What is the maximum current in a straight, 3.0-mm-diameter superconducting niobium wire?

What are the magnetic fields at points a to c in FIGURE EX29.13? Give your answers as vectors.

A 100 A current circulates around a 2.0-mm-diameter superconducting ring. What is the ring's magnetic dipole moment?

A 100 A current circulates around a 2.0-mm-diameter superconducting ring. What is the on-axis magnetic field strength 5.0 cm from the ring?

The on-axis magnetic field strength 10 cm from a small bar magnet is 500 μT. What is the on-axis field strength 15 cm from the magnet?

What is the line integral of $\overrightarrow{B}\cdot \overrightarrow{ds}$ between points i and f in FIGURE EX29.19?

The value of the line integral of $\overrightarrow{B}\cdot \overrightarrow{ds}$ around the closed path in FIGURE EX29.21 is 1.38 x 10^-5 T m. What are the direction (into or out of the figure) and magnitude of I₃?

A proton moves in the magnetic field B = 0.50 î T with a speed of 1.0 x 10⁷ m/s in the directions shown in FIGURE EX29.27. For each, what is magnetic force F on the proton? Give your answers in component form.

Radio astronomers detect electromagnetic radiation at 45 MHz from an interstellar gas cloud. They suspect this radiation is emitted by electrons spiraling in a magnetic field. What is the magnetic field strength inside the gas cloud?

To five significant figures, what are the cyclotron frequencies in a 3.0000 T magnetic field of the ions (a) O₂⁺, (b) N₂⁺, and (c) CO⁺? The atomic masses are shown in the table; the mass of the missing electron is less than 0.001 u and is not relevant at this level of precision. Although N₂⁺ and CO⁺ both have a nominal molecular mass of 28, they are easily distinguished by virtue of their slightly different cyclotron frequencies. Use the following constants: 1 u = 1.6605 x 10⁻²⁷ kg, e = 1.6022 x 10⁻¹⁹ C.

The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit the magnetic field at 2.4 GHz, and as they do so they emit 2.4 GHz electromagnetic waves. What is the magnetic field strength?

The Hall voltage across a conductor in a 55 mT magnetic field is 1.9 μV. When used with the same current in a different magnetic field, the voltage across the conductor is 2.8 μV. What is the strength of the second field?

The two 10-cm-long parallel wires in FIGURE EX29.33 are separated by 5.0 mm. For what value of the resistor R will the force between the two wires be 5.4 x 10⁻⁵ N?

FIGURE EX29.37 is a cross section through three long wires with linear mass density 50 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are attached to a table. What current I will allow the upper wire to 'float' so as to form an equilateral triangle with the lower wires?

What is the magnitude of the torque on the current loop in FIGURE EX29.39?

What is the loop's equilibrium orientation?

A small bar magnet experiences a 0.020 N m torque when the axis of the magnet is at 45° to a 0.10 T magnetic field. What is the magnitude of its magnetic dipole moment?

A long wire carrying a 5.0 A current perpendicular to the xy-plane intersects the x-axis at x = -2.0 cm. A second, parallel wire carrying a 3.0 A current intersects the x-axis at x = +2.0 cm. At what point or points on the x-axis is the magnetic field zero if (a) the two currents are in the same direction and (b) the two currents are in opposite directions?

When seen from the end, three long, parallel wires form an equilateral triangle 6.0 cm on a side. The wires each carry a 5.0 A current, with one current direction opposite the other two. What is the magnetic field strength at the center of the triangle?

Find an expression for the magnetic field strength at the center (point P) of the circular arc in FIGURE P29.45.

Each turn of a solenoid is a current loop with a magnetic dipole moment. Consider a 200-turn cylindrical solenoid that has an interior volume of 40 cm³ and for which each turn is a magnetic dipole moment with magnitude 8.0 x 10^-4 A m². What is the magnetic field strength inside the solenoid?

The earth's magnetic field, with a magnetic dipole moment of 8.0 x 10²² A m², is generated by currents within the molten iron of the earth's outer core. Suppose we model the core current as a 3000-km-diameter current loop made from a 1000-km-diameter 'wire.' The loop diameter is measured from the centers of this very fat wire. What is the current density J in the current loop?

The heart produces a weak magnetic field that can be used to diagnose certain heart problems. It is a dipole field produced by a current loop in the outer layers of the heart. What is the magnitude of the heart's magnetic dipole moment?

What is the magnetic field strength at the center of the semicircle in FIGURE P29.53?

The toroid of FIGURE P29.54 is a coil of wire wrapped around a doughnut-shaped ring (a torus). Toroidal magnetic fields are used to confine fusion plasmas. Is a toroidal magnetic field a uniform field? Explain.

A flat, circular disk of radius R is uniformly charged with total charge Q. The disk spins at angular velocity ω about an axis through its center. What is the magnetic field strength at the center of the disk?

A long, hollow wire has inner radius R₁ and outer radius R₂. The wire carries current I uniformly distributed across the area of the wire. Use Ampère's law to find an expression for the magnetic field strength in the three regions 0 < r < R₁, R₁ < r < R₂, and R₂ < r.

A proton moving in a uniform magnetic field with ${\vec{v}}_1=(1.00\times {10}^6\hat{i})\text{m/s}$ experiences force ${\vec{F}}_1=(1.20\times {10}^{-16}\hat{k})\text{N}$. A second proton with ${\vec{v}}_2=(2.0\times {10}^6\hat{j})\text{m/s}$ experiences ${\vec{F}}_2=(-4.16\times {10}^{-16}\hat{k})\text{N}$ in the same field. What is $\vec{B}$? Give your answer as a magnitude and an angle measured counter-clockwise from the $+x$-axis.