The magnetic field due to the loop always opposes the external magnetic field.(b) The flux due to the loop always has the opposite sign as the flux due to the external magnetic field.(c) The flux due to the loop always opposes the change in the flux due to the external magnetic field

C

Explanation:

The flux due to the loop always opposes the change in the flux due to the external magnetic field. This occurs as a result of the current that is induced in a coil (due to a magnetic flux change through the coil) which will always be in such that it opposes the change that caused it. ... Any induced current in a coil will result in a magnetic flux that is opposite to the original changing flux. This was what  Faraday was explaining in the law of Induction

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.