Option 1: The earth`s magnetic field is indeed due to the motion of metals like iron and nickel in the core of the earth. This motion generates electric currents, which in turn create the magnetic field.

Option 2: This statement is incorrect. The magnetic field lines of force are actually closer to one another near the poles of a magnet, not widely separated. In fact, the density of field lines is highest near the poles.

Option 3: This statement is correct. The flux density is defined as the amount of magnetic flux passing through a given area. If the cross-sectional area increases while the flux remains the same, the flux density will indeed decrease.

Option 4: This statement is correct. When a conductor moves through a magnetic field, a voltage is induced in the conductor. This induced voltage is directly proportional to the speed at which the conductor is moving through the field. Therefore, when the speed increases, the induced voltage also increases.

In conclusion, the correct answer is option 2, as the magnetic field lines of force are closer to one another near the poles of a magnet, not widely separated.