The gravitational force extend by a large, object, such as earth is

The gravitational force of an object with a LARGE MASS is stronger than the gravitational force of an object with less mass. Their size doesn't really matter. It's the mass.

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.