Current running through drain and source on an N channel MOSFET when the Vgs has not been met

Question

I am attempting to create an electromagnetic paper airplane launcher. I am using a hall effect sensor to detect when a sled is passing a solenoid. I am using an Arduino Uno as my microcontroller so that once the hall effect sensor detects a magnetic field, an output voltage would be supplied to the gate pin on a logic-level n channel MOSFET.

As a safety feature, I have added a push-button. In my Arduino code, I am only allowing for the MOSFET to receive an input voltage once the button is being pressed and the hall effect sensor reads a magnetic field.

I tested everything today and found that current will be supplied to the solenoids as intended, but it will also be supplied when a magnetic field is present without having the button pressed.

I am not sure if this is a coding problem or not. Before hooking the solenoid to the mosfet, I used an led in place of it in order to see if anything was being sent through the MOSFET. When I used the LED, it worked as intended--only turning on when a magnetic field was present and the button was pressed down.

I was just wondering if anyone knew what might be happening when I changed the LED with a copper wire solenoid.

Here is my code:

int coil=1;//solenoid 1
int hs=2;//1st hall effect sensor

int button=3;

int coil2=4;//solenoid 2
int hs2=5;//2nd hall effect sensor


void setup() {
//establishes the hall effect sensor pins as input, the button pin as input, and the solenoid pin as output
pinMode(hs, INPUT);
pinMode(coil, OUTPUT);

pinMode(hs2, INPUT);
pinMode(coil2, OUTPUT);

pinMode(button, INPUT);
}

void loop() {
  if ((digitalRead(button)==HIGH)&&(digitalRead(hs)==LOW))//makes sure that the mosfet will only send current to solenoid once the button has been 
  {                                                       //been pressed and the hall effect sensor has been triggered.
    digitalWrite(coil, HIGH);
  }
  else{
    digitalWrite(coil, LOW); 
  }

  if(digitalRead(hs2)==LOW)
  {
    digitalWrite(coil2,HIGH);
  }
  else{
    digitalWrite(coil2, LOW); 
  }

}