What is an anomaly? ( in physics if that )

In physics, quantum mechanics, and quantum field theory, an anomaly is a breaking of a symmetry which exists at the classical level. Anomalous global symmetries are often consistent, but anomalous gauge symmetries are usually inconsistent. ;)

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.