The shape of a magnet significantly influences the pattern of its magnetic field lines. In a bar magnet, the lines emerge from the north pole, curve around the magnet, and enter the south pole, creating a distinct pattern of loops. In ring-shaped or circular magnets, field lines form circular loops inside the magnet and stretch out from one face to the opposite, similar to a bar magnet. The geometry of the magnet affects the distribution and curvature of the field lines, which in turn influences the magnetic field's strength and uniformity at different points around the magnet.

Magnetic field lines can indeed be used to compare the relative strength of two magnets. By observing the density and spread of the field lines around each magnet, one can infer their relative strengths. A magnet with more closely packed field lines near its surface indicates a stronger magnetic field compared to a magnet with more widely spaced lines. However, this method provides a qualitative comparison rather than a precise quantitative measurement. For accurate measurements, instruments like a Gaussmeter are required, but field line patterns offer a useful initial assessment of relative magnetic strengths.

Magnetic field lines are a conceptual tool used to visualize and represent magnetic fields; they do not exist independently of the fields they depict. Therefore, it is not possible to have a magnetic field without field lines in a theoretical or illustrative sense. Similarly, magnetic field lines cannot exist without a magnetic field, as they are merely representations of the field's direction and strength. In essence, the presence of magnetic field lines is always indicative of an underlying magnetic field, and they cannot be observed or conceptualized separately from the field they represent.

The strength of a magnetic field decreases with increasing distance from a magnet, as does the density of the magnetic field lines. Near the magnet, the field lines are closer together, indicating a stronger magnetic field. As the distance increases, the field lines spread out and become less dense, signifying a weaker field. This pattern reflects the inverse square law, which states that the strength of a magnetic field is inversely proportional to the square of the distance from the source. Therefore, at greater distances, the magnetic influence weakens significantly, and the field lines become sparse and less pronounced.

Magnetic field lines never intersect each other because at each point in space, the magnetic field has a unique direction. If the field lines were to intersect, it would imply two different directions of the magnetic field at a single point, which is physically impossible. The field lines represent the direction of the magnetic force exerted at any given point in space. Since a magnetic field can only have one direction at any point, the lines depicting these fields cannot cross each other, ensuring that each line is a distinct path indicating the field's direction.