how to join two tables in database Laravel

I'm trying to join two tables (products table and Images table), so in products table each product has multiple images(stored in a row named image) so I want to display images of each product in images table. In images table I have a foreign key named product_id references(id) on products table, The problem is it can't store images in images table,(it keeps storing images in the row(image) in products table). How do I solve this?

Codes

Product.php

public function images()
 {
   return $this->hasMany('App\Image', 'product_id');
 }

Image.php

public function product()
{
  return $this->belongsTo('App\Product','product_id');
 }

Controller

 public function store(Request $request) 
 { 

$Input=$request->all();
$image=array();
if($files=$request->file('image')){
foreach($files as $file){
    $name=$file->getClientOriginalName();
    $file->move('images',$name);
    $image[]=$name;
  }
  } 
 product::create(array_merge($Input,
 [
 'image' => json_encode($image),

 ])); 
return redirect()->back(); 

}

Any help will be appriciated.

via Chebli Mohamed