Why would you need a component that creates a magnetic field within a circuit? What purpose do they serve and where would the common applications of inductors be?
1- You don't! Inductors are not used to create magnetic fields in circuitry. They do incidentally create fields, (often tiny, sometimes not) which we try to keep contained and hidden, but they are used for their circuit properties, not their magnetic field.
2- Inductors have circuit properties that a) resist changes in current; b) cause phase difference between AC currents and voltages. This means they discriminate between different frequencies of AC (the frequency tells you haw fast the current is changing.) Inductors resist high frequencies.
On the whole they are used mainly for radio frequencies, because inductors for audio frequencies need to be bigger and smaller capacitors can do the job.
3- So they are used to select or block different frequencies in eg. audio filters and radio tuners. In combination with a capacitor (resists low frequencies) they produce a circuit tuned to one specific frequency. Loudspeakers often have inductors (and capacitors) to separate the current to the woofer from that for the tweeter.
They are often put in power supply leads, to pass the low 50Hz mains, but block higher frequency interference (sometimes this is in the form of ferrite blocks clamped to the lead.) Electric motors (DC or universal) often have 2 small inductors wired in series with their leads to block any high frequency interference generated by brush sparks or fast switching (and a capacitor in parallel to short circuit them.)