29. Sources of Magnetic Field

A set of Helmholtz coils (see Problem 62, Fig. 28–61) have a radius 𝑅 = 10.0 cm and are separated by a distance 𝑅 = 10.0 cm . Each coil has 85 loops carrying a current I = 2.0 A. Graph B as a function of 𝓍.

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.)

Determine the field strength at the center of a current-carrying square loop having sides of length 2R.

(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?

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?

A small solenoid (radius r_a) is inside a larger solenoid (radius r_b > r_a). They are coaxial with n_a and n_b turns per unit length, respectively. The solenoids carry the same current, but in opposite directions. Let r be the radial distance from the common axis of the solenoids. If the magnetic field inside the inner solenoid (r < r_a) is to be in the opposite direction as the field between the solenoids (r_a < r < r_b), but have half the magnitude, determine the required ratio n_b/n_a.