How does the strength of a magnetic field around a wire vary?

By pointing one's right thumb along the direction of the current, the direction of the magnetic field can by found by curving one's fingers around the wire. The strength of the magnetic field depends on the current I in the wire and r, the distance from the wire.

a.

explanation:

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.