Particle movement through a magnetic field

Hello,

My current code is moving particles in a straight line. The goal is simulate their movement through a magnetic and electric field depending on many variables. I will worry about the scaling later on when the physics are working properly. I provided my current coding for this scripted movement and a list of equations that are being used within it. The last picture is the goal that my simulation is working towards. The arcs within the movement is caused by a magnetic field turning a particles path in a circular motion. My simulation is within 3D space. I linked the images within a comment below.

I appreciate any input! Thanks!

    float Radius;
    public Rigidbody rb;
    public float Constant;
    public float Charge;
    public float B;
    float P;
    public float Px;
    public float py;
    public float Pz;
    float Omega;
    float Velocity;
    float time;
    float delta_time;
    public float delta_min;
    public float delta_max;
    float px_dt;
    float pz_dt;


    private void Start()
    {
    
        rb = GetComponent<Rigidbody>();
        time = Time.deltaTime;

        P = Mathf.Sqrt(Mathf.Pow(Px, 2) + Mathf.Pow(Pz, 2));
        Radius = (Constant * P) / (B * rb.mass);
        Velocity = P / rb.mass;
        Omega = Velocity / Radius;
     

    }

    private void FixedUpdate()
 
    {
        delta_time = Mathf.Lerp(delta_min, delta_max, time);

        px_dt = Mathf.Cos(Omega * delta_time) * Px * time + Mathf.Sin(Omega * delta_time) * Pz * time;
        pz_dt = -Mathf.Sin(Omega * delta_time) * Px * time + Mathf.Cos(Omega * delta_time) * Pz * time;

        transform.Translate(px_dt, py,  pz_dt);
    }
}