A small solenoid (radius ra) is inside a larger

Chapter 28, Problem 28.71

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A small solenoid (radius ra) is inside a larger solenoid(radius rb > ra). They are coaxial with n a and nb turns perunit length, respectively. The solenoids carry the samecurrent, but in opposite directions. Let r be the radialdistance from the common axis of the solenoids. If themagnetic field inside the inner solenoid (r < ra) is to be inthe opposite direction as the field between the solenoids(ra < r < rb), but have half the magnitude, determine therequired ratio nb/ n a.

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