解答---**Question Stem:**
利用电磁场实现离子偏转是科学仪器中广泛应用的技术。某探究学习小组设计了如下一套实验装置, 其俯视图如图所示, M、N 是长为 L、相距很近的网状极板(由金属丝组成的网状电极), 极板 M 上方存在磁感应强度大小为 $B_1=B_0$, 方向垂直纸面向里的匀强磁场, 极板 N 下方存在磁感应强度大小为 $B_2=kB_0$ (k 大小可调), 方向垂直纸面向外的匀强磁场, 极板 M、N 之间区域无磁场, 极板 M、N 间电压 $U_{MN}$ ($U_{MN}>0$) 大小可调。在极板 M 中点上方距离为 d (L 与 d 满足 L=3d) 的位置放置一离子源 A, 其由两部分离子源组成, 可同时向右发射负电离子和向左发射正电离子, 单位时间内正负离子的发射数目均 为 N, 正负离子电荷量和质量大小均为 q 和 m, 发射速度 v 大小可调。在极板 N 下方紧贴着相距为 L 的两块足够大平行金属板, 两板可接电流计。极板 M、N 间距忽略不计, 忽略场的边界效应、离子受到的重力及离子间相互作用。
**Questions:**
(1) 当 $v=v_0$ 时, 离子恰好垂直极板 M 进入 M、N 间, 求 $B_0$ 的大小;
(2) 当 $v=\frac{2}{3}v_0$, $U_{MN}=\frac{mv_0^2}{9q}$, $k=2$ 时, 正、负离子在 $B_2$ 磁场中运动的半径之比;
(3) 当 $v=v_0$, $k=3$, 闭合开关 S, 不计电流计内阻, 画出电流计示数 $I_1$ 与极板 M、N 间电压 $U_{MN}$ 的关系图;
(4) 闭合开关 S, 若电流计内阻可忽略, 当 $v=v_0$, $U_{MN}=\frac{3mv_0^2}{2q}$, $k=2$ 时, 求电流计示数 $I_2$ 与电流计内阻 R 的关系。
**Chart/Diagram Description:**
* **Type:** Schematic diagram illustrating an experimental setup involving charged particle motion in electric and magnetic fields. It's a top-down (俯视图) view as stated in the text.
* **Main Elements:**
* **Ion Source A:** Located above the plate M, represented by a circle labeled 'A'. There is an upward-pointing arrow from A, implying initial velocity direction is downwards in the diagram's context relative to the text description, but the text says it emits to the right (negative ions) and left (positive ions). The diagram shows the setup viewed from above, so 'right' and 'left' are horizontal directions in the plane of the diagram. A is positioned above the midpoint of M, at a distance d from M.
* **Plate M:** A horizontal line labeled 'M', representing the upper grid plate. It has length L.
* **Plate N:** A horizontal line labeled 'N', parallel to M and located below M, representing the lower grid plate. It also has length L. The distance between M and N is described as very small.
* **Magnetic Field B1:** Region above plate M, indicated by a dashed rectangle above M. This region is filled with 'x' symbols, indicating the magnetic field $B_1$ is directed perpendicularly into the page. The text states $B_1 = B_0$.
* **Magnetic Field B2:** Region below plate N, indicated by a dashed rectangle below N. This region is filled with '.' symbols, indicating the magnetic field $B_2$ is directed perpendicularly out of the page. The text states $B_2 = kB_0$.
* **Region between M and N:** No magnetic field is present in this region.
* **Lower Parallel Plates:** Two larger parallel horizontal plates located below N. These plates are separated by a distance L and are aligned with the plates M and N. These plates are connected via wires to a galvanometer G and a switch S.
* **Galvanometer G:** Represented by a circle with 'G' inside, connected in the circuit with the lower plates and switch S.
* **Switch S:** Represented by a standard switch symbol, connected in series with G and the lower plates.
* **Labels and Annotations:**
* L: Length of plates M and N, and also the distance between the lower parallel plates.
* d: Distance from ion source A to plate M.
* $B_1$: Label for the magnetic field region above M.
* $B_2$: Label for the magnetic field region below N.
* A: Label for the ion source.
* M: Label for the upper grid plate.
* N: Label for the lower grid plate.
* G: Label for the galvanometer.
* S: Label for the switch.
* "第 18 题图": Figure label at the bottom.
* **Relative Position and Direction:** Ion source A is positioned above the midpoint of M. M is above N. The B1 field is above M (into page). The B2 field is below N (out of page). The region between M and N is empty (no field). The lower plates are below N and span the length L, connected to G and S.