Solenoids and Toroids
Core Sentence / 核心句
Solenoids and toroids use many current turns to concentrate magnetic field into controlled regions.
中文理解：多匝电流把每一匝产生的磁场叠加，使 magnetic field 主要集中在线圈内部或环形 core 中。
Long Solenoid / 长螺线管
turn density：
right-hand fingers curl with current；thumb gives internal field direction。
Toroid / 环形螺线管
core 内：
ideal model：
- central hole：；
- core：nonzero, approximately confined；
- outside：。
Approximations / 近似条件
- solenoid must be long relative to radius；
- toroid assumed tightly wound；
- leakage and fringing fields neglected；
- linear core represented by 。
Watch Out / 易错点
- distinguish total turns from turns per length 。
- solenoid uses ，not when is total turns。
- toroid contains 。
- toroid field generally varies as 。
- outside field is approximately, not universally exactly, zero。