Field Strength and Force
The stronger the field the greater is the force exerted on objects within that field. Irrelevant to what field we are talking about, the stronger the field is the more force it can apply on objects within it. For example, the bigger an object in space the bigger the gravitational field and it attracts objects at it at a much faster rate. Likewise the bigger the magnet the more magnetic objects it will pull at a larger distance.
The moon will pull you towards itself with a smaller force than the Earth
The bigger magnet will pull a nail towards it faster than the smaller one
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