写入二进制文件不起作用

下面的代码可以编译并成功运行，但是在退出时没有任何写入文件。创建文件后，选择注册时询问所有详细信息并显示消息注册成功。文件为customers.data空（文件大小为0kb）。该函数write不会将对象写入文件。代码中的所有内容似乎都是正确的。无法识别错误。请帮忙

主程序：

int main()
{
    int ch;
    Customer cust;
    fstream file;
    file.open("customers.data",ios::out|ios::app|ios::binary);
    if(!file)
    {
        cout<<"\nError Files are missing. Unable to create files\n";
        system("pause");
        exit(1);
    }
    cout << "WELCOME! Press any key to continue.\n\n";
    system("pause");
    do
    {
        system("cls");
        cout<<"\n\n\n";
        cout<<"1->Login"<<endl;
        cout<<"2->Register"<<endl;
        cout<<"3->Exit"<<endl;
        cout<<"Choose An option: ";
        cin>>ch;
        switch(ch)
        {
        case 1:
            if(cust.Login()==true)
            {
                LaunchCustomerMenu();
            }
            else
            {
                cout<<"Incorrect Email/Password\n";
                system("pause");
            }

            break;
       case 2:
        cust.Register();
        file.write((char*)&cust, sizeof(cust)); //does not work
        if(!file.fail()) //still true
        {
            cout<<"\n\nRegistration Successful"<<endl;
            system("pause");
        }
         else
            {
                cout<<"\nTheir was a Error processing your Registration\n";
                system("pause");
            }

            break;
        case 3:
            exit(0);
            break;
        default:
            cout<<"\n\nWRONG OPTION\n";
            cout<<"Choose Again\n\n";
            system("pause");
        }
        cin.ignore();
    }
    while(ch!=3);
    file.close();
    return 0;
}

班级：

class Customer
{
private:
    unsigned int CustomerID;
    string CustomerName;
    string CustomerAddress;
    string CustomerEmail;
    string CustomerPassword;
    unsigned int CustomerPhone;
public:
    Customer();

    void Register();
    bool Login();

    unsigned int getID();
    string getName();
    string getEmail();
    string readPassword();
    unsigned int getPhone();
    unsigned int RandomID();

    void modifyName();
    void modifyAddress();
    void modifyEmail();
    void modifyPassword();
    void modifyPhone();
};

CustomerID 是随机生成的。

功能寄存器：

void Customer::Register()
{
    cout<<"Enter Your Name: ";
    cin.ignore();
    getline(cin,CustomerName);
    cout<<"Enter Your Address: ";
    cin.ignore();
    getline(cin,CustomerAddress);
    cout<<"Enter Your Email: ";
    cin>>CustomerEmail;
    cout<<"Enter A Password: ";
    cin.ignore();
    getline(cin,CustomerPassword);
    cout<<"Enter Your Phone no. :";
    cin>>CustomerPhone;
}

编辑：根据下面的答案，我添加了一个检查，file.fail()但它返回false并且customers.data为空，即write操作无法写入对象。