帮我看看这道题怎么解---**Extraction Content:** **Problem 20** (12 分) 我国“天宫”空间站采用霍尔推进器控制姿态和修正轨道. 图为某种霍尔推进器的放电室 (两个半径接近的同轴圆筒间的区域) 的示意图. 放电室的左、右两端分别为阳极和阴极, 间距为 $d$. 阴极发射电子, 一部分电子进入放电室, 另一部分未进入. 稳定运行时, 可视为放电室内有方向沿轴向向右的匀强电场和匀强磁场, 电场强度和磁感应强度大小分别 为 $E$ 和 $B_1$; 还有方向沿半径向外的径向磁场, 大小处处相等. 放电室内的大量电子可视为处于阳极附近, 在垂直于轴线的平面绕轴线做半径为 $R$ 的匀速圆周运动 (如截面图所示), 可与左端注入的氙原子碰撞并 使其电离. 每个氙原子的质量为 $M$、电荷量为 $+e$, 初速度近似为零. 氙离子经过电场加速, 最终从放电 室右端喷出, 与阴极发射的未进入放电室的电子刚好完全中和. 已知电子的质量为 $m$、电荷量为 $-e$; 对于氙离子, 仅考虑电场的作用. **Diagram Description:** The image contains three diagrams. The leftmost diagram is a cross-section of the discharge chamber. It shows two concentric circles representing the inner and outer walls of the chamber. The region between the circles is labeled as the "Discharge Chamber". An axis is shown horizontally, labeled "Axis". An electron is depicted moving in a circular path within the discharge chamber. A radial magnetic field $B_2$ is shown pointing outwards from the axis. A uniform magnetic field $B_1$ is shown pointing along the axis to the right. The middle diagram shows a side view of the discharge chamber. It is a cylindrical region between an Anode on the left and a Cathode on the right, separated by a distance $d$. A uniform electric field $E$ is shown pointing from the Anode to the Cathode (left to right). A uniform magnetic field $B_1$ is shown pointing from left to right along the axis. A radial magnetic field $B_2$ is shown pointing outwards from the axis. Electrons are shown being emitted from the Cathode, with some entering the chamber and some not. Xenon atoms are shown entering from the left (near the Anode). Xenon ions are shown accelerating to the right and exiting the chamber. An electron trajectory in a circular path is shown within the chamber near the Anode. The radius of this circular motion is labeled as $R$. The rightmost diagram is another cross-section of the discharge chamber, similar to the leftmost one, showing the radius $R$. It is labeled "Axial view". **Given Information:** * Anode and Cathode are separated by distance $d$. * Discharge chamber has a uniform electric field $E$ along the axis (left to right). * Discharge chamber has a uniform magnetic field $B_1$ along the axis (left to right). * Discharge chamber has a radial magnetic field $B_2$ pointing outwards from the axis. $B_2$ is uniform in magnitude. * Large number of electrons in the discharge chamber are near the Anode and perform uniform circular motion with radius $R$ in the plane perpendicular to the axis. * Xenon atoms are injected from the left (near Anode) with initial velocity approximately zero. * Xenon atoms are ionized by collision with electrons. * Mass of xenon atom/ion: $M$. Charge of xenon ion: $+e$. * Xenon ions are accelerated by the electric field. * Xenon ions exit from the right end of the discharge chamber and are neutralized by electrons emitted from the Cathode but not entering the chamber. * Mass of electron: $m$. Charge of electron: $-e$. * For xenon ions, only consider the effect of the electric field. **Questions:** (1) 求氙离子在放电室内运动的加速度大小 $a$; (Find the magnitude of the acceleration of a xenon ion moving in the discharge chamber $a$;) (2) 求径向磁场的磁感应强度大小 $B_2$; (Find the magnitude of the magnetic induction of the radial magnetic field $B_2$;) (3) 设被电离的氙原子数和进入放电室的电子数之比为常数 $k$, 单位时间内阴极发射的电子总数为 $n$, 求此霍尔推进器获得的推力大小 $F$. (Let the ratio of the number of ionized xenon atoms to the number of electrons entering the discharge chamber be a constant $k$. Let the total number of electrons emitted by the cathode per unit time be $n$. Find the magnitude of the thrust obtained by this Hall thruster $F$.)