A solenoid of length 20cm with 400 turns carries a current of 2A and encloses a soft-iron core. After the core is removed, the magnetic field inside the solenoid becomes one-tenth of its former value.
a. Keeping the current and length unchanged, calculate the number of turns required in a new winding to restore the original magnetic field.
b. In one sentence, state why the magnetic field decreased when the core was removed.