解析这道题---**Extraction Content:** 15. (18 分) 如图 13, 空间中有两块带电平行金属板 M、N, 两板间距为 d = 0.5m, 两板间的电压 U_MN = 6V。一可视为质点的小球以 v₀ = 3m/s 的水平速度从紧靠 M 板的 A 点飞入, 从下极板的右端点 B 点飞出, 并沿切线方向飞入竖直光滑圆轨道。B 点与光滑竖直圆轨道平滑连接, 圆轨道的半径 R = 1m。平行金属板 M、N 的右侧垂线 CD 的右侧区域存在水平向右的匀强电场, 电场强度大小 E = 15N/C。已知小球带正电, 质量 m = 1.0kg, 电荷量 q = 0.5C, 重力加速度 g 取 10m/s², sin37° = 0.6, 不计空气阻力。求: (1) 小球在 B 点的速度大小 v_B; (2) 极板的长度 L; (3) 小球在竖直圆轨道上滚动的最大速度 v_m 的大小为多少? **Chart/Diagram Description:** * **Type:** Physics problem diagram illustrating the motion of a charged particle in electric and gravitational fields, including motion between parallel plates and subsequent motion on a vertical circular track. * **Main Elements:** * Two horizontal parallel plates labeled M (upper) and N (lower). * A point A on the left side, close to plate M, with an initial horizontal velocity v₀ pointing right. * A point B on the right side, on plate N. * A curved trajectory shown from A to B. * A vertical dashed line labeled CD on the right side, extending vertically from above M to below N. C is above M, D is below N. * Horizontal arrows to the right of the line CD, representing a uniform electric field E pointing horizontally to the right. * A vertical circular track connected smoothly at point B. * The center of the circle is labeled O. * The radius of the circle is labeled R, extending from O to B. * A point E is marked on the circular track. * The distance between plates M and N is indicated as d. * The initial velocity at A is labeled v₀. * The velocity at B is labeled v_B. * A reference frame or implied coordinate system is suggested by the horizontal velocity v₀ and vertical motion between the plates, and the vertical circular track. The line CD appears to be a boundary for the electric field. * The diagram is labeled "图 13".