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Problem 3
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)?
Problem 6
What is the magnetic field at the position of the dot in FIGURE EX29.6? Give your answer as a vector.
Problem 8
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?
Problem 13
What are the magnetic fields at points a to c in FIGURE EX29.13? Give your answers as vectors.
Problem 16a
A 100 A current circulates around a 2.0-mm-diameter superconducting ring. What is the ring's magnetic dipole moment?
Problem 16b
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?
Problem 17b
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?
Problem 19
What is the line integral of between points i and f in FIGURE EX29.19?
Problem 21
The value of the line integral of 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?
Problem 27
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.
Problem 28
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?
Problem 29
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.
Problem 31a
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?
Problem 32
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?
Problem 33
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?
Problem 37
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?
Problem 39a
What is the magnitude of the torque on the current loop in FIGURE EX29.39?
