# If inductor can store energy why not a current carrying wire?

My book says that an inductor produces magnetic field around it and it stores energy in this field but then i thought a current carrying wire also produces magnetic field around it then why does it not store energy ? And if it does then why do we use inductors ?

A straight wire carrying a current does indeed store energy in a magnetic field so it does have an inductance. For example see Derivation of self-inductance of a long wire.

However the inductance of a straight wire is very small. Coiling the wire into a solenoid allows you to create a circuit element with a large inductance for a small size.

The inductance of a straight wire is given by:

$$L_\text{wire} = \frac{\mu\ell}{8\pi} \tag{1}$$

The inductance of a coiled wire is normally written in the form:

$$L_\text{coil} = \frac{\mu N^2 A}{d}$$

where $N$ is the number of turns in the coil, $A$ is the area of the coil and $d$ is the length of the coil. To compare this with equation (1) we note that $A=C^2/4\pi$ where $C$ is the circumference, and $NC$ is the total length of the wire. Substituting this into the equation above gives:

$$L_\text{coil} = \frac{\mu \ell^2}{4\pi d} \tag{2}$$

Or we for comparison with equation (1) we could use $\ell=N2\pi r$ to rewrite this as:

$$L_\text{coil} = \frac{\mu \ell}{2}\frac{Nr}{d} \tag{3}$$

• To clarify, is the inductance of (say) 100m of wire constant, irrespective of whether it is straight or coiled? – user56903 Sep 28 '16 at 14:59
• Thank you ! I just want o ask one more question. My book also says that some energy by the battery is spent in working against the induced emf of the inductor and that energy is stored in magnetic field . So if wire also stores energy in magnetic field then against what do we spend energy that is stored in the magnetic field of the wire as in the case of inductors we spend energy against the emf ? Does wire also have an induced emf ? – Varun Chandra Sep 28 '16 at 15:06
• @VarunChandra: Yes, but the inductance of a straight wire is so small that under normal circumstances it can be ignored. – John Rennie Sep 28 '16 at 15:16
• @JohnRennie: But how can a straight wire have an emf induced in it? , I mean there has to be some changing magnetic flux through the wire for inducing emf and a wire is not a closed curve through which I can associate magnetic flux – Varun Chandra Sep 28 '16 at 15:33
• @VarunChandra The complete circuit is always a closed curve, otherwise current can't flow around it. If you try to think about "a straight wire carrying current" but ignore how the current gets into one end of the wire and out of the other, you are leaving out an important part of the physics. For a coiled wire inductor you can ignore the rest of the circuit, because the inductance of the connecting wires will (usually) be small compared with the inductor itself. – alephzero Sep 29 '16 at 1:00