The difference between the third and fourth ionization energies of scandium is much larger than the difference between the third and fourth ionization energies of titanium. why?

This is because removing three electrons means third ionization energy would leave scandium with a full valence shell that is 3s²3p⁶ and removing a fourth electron would begin to remove electrons from a full valence shell which is very energetically not favorable.

Removing a third and fourth electron from titanium is bringing Ti closer and closer to having an empty 4th energy level and a completely full 3rd energy level. Removing the 4th electron would be very energetically favorable because it would result in a full valence shell.

adding a(n) to an electric circuit would increase the magnetic field around a wire;

b. solenoid

a solenoid is a type of electromagnet whose purpose is to generate a controlled magnetic field.

if the purpose of the solenoid is instead to impede changes in the electric current, a solenoid can be more specifically classified as an inductor rather than an electromagnet.