29. Sources of Magnetic Field

The single loop below has a radius of 10 cm and is perpendicular to the page (shown at a slight angle so you can better visualize it). If the magnetic field at the center is 10^-6 T directed left, what is the magnitude of the current? What is the direction of the current at the top of the wire:into the page (towards left) or out of the page (towards right)?

A long wire having total resistance of 10 Ω is made into a solenoid with 20 turns of wire per centimeter. The wire is connected to a battery, which provides a current in order to produce a 0.04 T magnetic field through the center of the solenoid. What voltage must this battery have?

The two tightly wound solenoids below both have length 40 cm and current 5 A in the directions shown. The left solenoid has radius 20 cm and 50 m of total wire. The right solenoid has radius 0.5 m and 314 m of total wire. The thinner solenoid is placed entirely inside the wider one so their central axes perfectly overlap. Assume wires don't touch. What is the magnitude and direction of the magnetic field that is produced by a combination of the two solenoids at their central axis?

(Note:your worksheet may have a typo and say "0.5 cm"for the right solenoid's radius; it should be 0.5 m.)

A thin 12-cm-long solenoid has a total of 370 turns of wire and carries a current of 2.0 A. Calculate the field inside the solenoid near the center."

(I) A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.4 A, how many turns must the solenoid have?

(II) A 650-turn horizontal solenoid is 15 cm long. The current in its loops is 38 A. A straight wire cuts through the center of the solenoid, along a 3.0-cm diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?