29. Sources of Magnetic Field

At what distance from a wire carrying a $10\mathrm{A}$ current is the magnetic field strength equal to $50\mathrm{\mu }\mathrm{T}$? This is the approximate value of the Earth's magnetic field.

Typical household wiring in the United States is 14-gauge copper wire which has a radius of $813\mathrm{\mu }\mathrm{m}$. What is the magnetic field strength inside the wire, halfway between the center and the outside edge, when it is carrying a typical household current of $10\mathrm{A}$?

A wire near the equator carries a current perpendicular to the Earth's magnetic field of $50\mathrm{\mu }\mathrm{T}$ in a location where the field is parallel to the ground and points straight north. Assuming it was of correct magnitude, what direction should the current be in to levitate the wire?

A wire near the equator carries a current perpendicular to the Earth's magnetic field of $50\mathrm{\mu }\mathrm{T}$ in a location where the field is parallel to the ground and points straight north. The wire has a mass per length of $5.9\mathrm{g}/\mathrm{m}$. What magnitude of current in the wire could balance it against the force of gravity? (This example is not very realistic. The mass per length given would be reasonable for a very thin wire which could not handle this large of a current for very long.)

Currents in dc transmission lines can be 100 A or higher. Some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers. For a line that has current 150 A and a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? Express your answer in teslas and as a percentage of the earth's magnetic field, which is 0.50 G. Is this value cause for worry?

An electromagnetic rail gun uses magnetic forces to launch projectiles. FIGURE P29.76 shows a 10-cm-long, 10 g metal wire that can slide without friction along 1.0-m-long horizontal rails. The rails are connected to a 300 V source, and a 0.10 T magnetic field fills the space between the rails. Each rail has linear resistivity ⋋ = 0.10 Ω/m, which means that the resistance is ⋋ multiplied by the length of rail through which current flows. Assume that the sliding wire and the left end, where the voltage source is, have zero resistance. The wire is initially placed at x₀ = 5.0 cm then the switch is closed. What is the wire's speed as it leaves the rails?

A 10 A current is charging a 1.0-cm-diameter parallel-plate capacitor.b. What is the magnetic field strength at a point 2.0 mm radially from the center of the capacitor?