流编写器未写入 webapi 中的 JSON 文件

我正try 使用WebAPI在JSON文件中写入数据，但流编写器没有将数据写入该文件.

JSON文件:

{
"Students": [
  {
  "id": 1,
  "name": "Ravi",
  "department": "IT"
  },

 {
  "id": 2,
  "name": "Raj",
  "department": "hr"
  },
{
  "id": 3,
  "name": "avi",
  "department": "it"
 },
{
  "id": 4,
  "name": "rome",
  "department": "HR"
 },
 {
  "id":5,
  "name": "virat",
  "department": "HR"
 },
 {
  "id":6 ,
  "name": "Tushar",
  "department": "RM"
 }
]
}

班级

     public class Student
{
    public int Id { get; set; }
    public string Name { get; set; }

    public string Department { get; set; }
}

    public class Students
{
    public List<Student> students { get; set; }
}   

API控制器:[HttpPost]向json文件写入数据的方法.

    [Route("api/[controller]")]
[ApiController]
public class StudentsController : ControllerBase
{

  [HttpPost]
    public IActionResult Add(Students _Student)
    {        
        using (var fs = new FileStream("C:/Users/tanmay_pawar/source/repos/CRUDAPI/CRUDAPI/people.json", FileMode.Append))
         using (var sw = new StreamWriter(fs))
        {
           sw.WriteLine(_Student);
        }

}

学生收到的数据不会添加到json文件中.