Why is Earth's magnetic field not strong? Why is Earth's magnetic field not as strong as the magnetic field that is artificially produced even though Earth's magnetic field is produced from an iron core that is very large? Wouldn't more iron mean a stronger magnetic field, so why is the Earth's magnetic field weaker than even a fridge magnet in that case?
 A: Except as an aid to intuition, it makes little sense to compare the strengths of Earth's magnetic field and a bar magnet. They are based on completely different physics. A bar magnet derives its field from ferromagnetism, an inherently quantum mechanical effect that is mainly based on electron spins. Ferromagnetism does not exist at the temperatures of Earth's core. Instead, Earth's magnetic field is generated by a dynamo effect, which is a complicated feedback loop involving electric currents, the ambient magnetic field, and the motion of a highly conducting fluid. There is virtually no overlap between the factors that affect the strength of the magnetic field in these two phenomena. However, it is worth pointing out that, whereas humans design bar magnets to optimize the magnetic field, Earth doesn't care how strong its magnetic field is.
A: Its because the movement of conductive (molten iron) material which gives rise to the dynamo effect is very sluggish.
A: In addition to what @nield Nielsen said, new studies have shown that the magnitude of a planet's magnetic field is dependent on the planet's rate of rotation. For instance, Jupiter rotates faster than Earth and has a stronger magnetic field than Earth, while Venus rotates slower than Earth and has a weaker magnetic field.
A: The answer to your question is the distance from the source.

For Earth's case, it turns out to be 1r3). And you can guess that it originates from the center of Earth. Since we're sitting pretty at ~6371km, adding another 100-1000 km would not even decrease it by half, let alone an order of magnitude.

What is the Earth's magnetic field in space?
Earth's magnetic field actually turns out to be quite strong at the source (core), but its strength falls off with the distance and at the surface it is very weak, as you say it is weaker then a bar magnet.
A: Sure, the magnetic field magnitude of Earth, which forms the magnetosphere, is small compared to say, a good bar magnet.  However, the magnetic moment of Earth is on the order of $\sim 8 \times 10^{22}$ $A \ m^{-2}$.  For comparison, the magnetic moment of a bar magnet is on the order of 1 $A \ m^{-2}$.  This is why you don't see magnetic anomalies from bar magnets when measuring Earth's magnetic field in space.
