29. Sources of Magnetic Field

A solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius b and outer radius c (Fig. E28.43). The central conductor and tube carry equal currents I in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. Derive an expression for the magnitude of the magnetic field (b) at points outside the tube (r > c).

As a new electrical technician, you are designing a large solenoid to produce a uniform 0.150-T magnetic field near the center of the solenoid. You have enough wire for 4000 circular turns. This solenoid must be 55.0 cm long and 2.80 cm in diameter. What current will you need to produce the necessary field?

A closed curve encircles several conductors. The line integral ∲B .dl around this curve is 3.83 * 10^-4 T m. (b) If you were to integrate around the curve in the opposite direction, what would be the value of the line integral? Explain.

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.

An infinitely wide flat sheet of charge flows out of the figure in FIGURE CP29.83. The current per unit width along the sheet (amps per meter) is given by the linear current density Jₛ. b. Find the magnetic field strength at distance d above or below the current sheet.

What is the line integral of →B ⋅ ds between points i and f in FIGURE EX29.19?

The value of the line integral of →B ⋅ 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?