请写出解答步骤，配上语音讲解---**Extraction Content:** **Problem Description:** 16. 某种粒子诊断测量装置简化装置图所示，竖直平面内在边界为矩形 CDEF，方向垂直纸面向内的匀强磁场，探测板 HK 的下端 K 在 EF 的右侧延长线上，该板平行于 DF 竖直放置，且能沿水平方向缓慢移动且接地。a、b、c 三束宽度不计的离子束持续从边界 EF 沿垂直 EF 方向射入磁场，a 束离子在磁场中偏转 143°后射出磁场，a、b 束离子射入磁场的速度大小分别为 v₀、0.75v₀，b、c 束离子在磁场中的运动时间均相同。已知 a、b、c 三束离子射入点距 F 的距离分别为 1.8R₀、0.3R₀、0.2R₀，三束离子每束每秒射入磁场的离子数均为 n，离子质量均为 m、电荷量均为 -q，探测板 HK 的长度为 0.8R₀，不计离子重力及离子间的相互作用，离子在磁场内、外均不会相撞，sin 37° = 0.6。 **(1) 求磁感应强度 B 的大小和 c 束离子在磁场中的运动时间 t₁;** **(2) 求无法探测到离子束时探测板与边界 DF 的最小距离 S_min;** **(3) 若打到探测板上的离子全部被吸收，探测板到 DF 距离为 S，求粒子束对探测板的平均作用力的水平分量 f。** **Chart/Diagram Description:** * **Type:** Schematic diagram of a particle detection setup involving a magnetic field region and a detector plate. * **Main Elements:** * **Region CDEF:** A rectangle labeled with vertices C, D, E, F. Represents a magnetic field region. CD and EF are horizontal boundaries, CE and DF are vertical boundaries. * **Magnetic Field:** Indicated by 'x' symbols uniformly distributed within the rectangle CDEF, signifying a uniform magnetic field directed perpendicular to the plane of the diagram, pointing inwards. * **Line Segment HK:** A vertical line segment labeled HK, representing a detector plate. It is positioned to the right of the rectangle CDEF, parallel to DF. Point K is located on the horizontal line extending from EF to the right. * **Points E, F, K:** E and F are corners of the rectangle CDEF on the bottom horizontal boundary. K is the bottom end of the detector HK, on the extension of the line EF. * **Points a, b, c:** Points labeled a, b, and c on the horizontal line EF, representing the entry points of three ion beams into the magnetic field. * **Arrows:** Vertical arrows originating from points a, b, and c, pointing upwards into the rectangle CDEF, indicating the initial velocity direction of the ion beams (perpendicular to EF). * **Labels H, D, C, E, F, K, a, b, c:** Labels identifying specific points or regions. * **Relative Position:** Rectangle CDEF is on the left. Line segment HK is to the right of CDEF and parallel to its right edge DF. E, F, and K are collinear on a horizontal line. a, b, c are on the line segment EF. **Other Relevant Text:** * sin 37° = 0.6 * Velocities of a, b beams: v₀, 0.75v₀ * Entry points a, b, c distances from F: 1.8R₀, 0.3R₀, 0.2R₀ * Ion beam properties: n particles per second per beam, mass m, charge -q. * Detector length: 0.8R₀. * Assumptions: Negligible gravity, no interaction between ions, no collisions inside or outside the magnetic field. * Given: a beam deflects 143° after exiting the magnetic field. b and c beams have the same travel time in the magnetic field.