Coil vs Solenoid: Understanding the Difference and Equations for Magnetic Fields

[henry3369]

Homework Statement

I'm having problems figuring out the difference between a coil and a solenoid. My book provides two equations for magnetic field, and they are similar, but one depends on the radius (coil) while the other depends on the length (solenoid).

Homework Equations

B_coil = μNI/2a (field at the center of N circular loops)
B_solenoid = μNI/L (field in a solenoid)

The Attempt at a Solution

As you can see, the B_coil depends on the a (radius) while the solenoid depends on L (length).

 

[rolotomassi]

A coil is just a current loop, which produces a B-field around it due to moving charge. Each loop will contribute equally to the flux so the B-field is proportional to the number of loops. The radius dependence can be intuitively understood if you imagine the radius going to infinity, then at the centre of the loop it is equivalent to there being no current loop at all, because it is so far away.

The field inside a solenoid is enhanced due to the lump of metal which the coil is wrapped around. There is a reason for this but I won't confuse the issue. This core, iron for example, amplifies the B-field produced by the coils wrapped around it. The field outside a solenoid is weak and so usually can be approximated as zero. Since the current loops produce magnetic flux lines, the more of them the stronger the B-field, the number of magnetic flux lines in a region depends on the concentration of coils in that region (same principle as the normal current loop).
This concentration is N/L. The B-field inside the solenoid is approximately constant.

For a more description you may want to look at Amperes Law and Biot-Savart Law as applied to your examples.

 

[rude man]

A "coil" as you understand it has essentially zero length. It can be a single-turn coil or many turns but then they have to be wound closely together so that the coil again has essentially zero length.
By contrast, a solenoid by definition has a long length.

In the case of the coil you get the B field by the Biot-Savart law. For solenoids you use Ampere's law.

 

[deepakkumaar97]

A "coil" as you understand it has essentially zero length. It can be a single-turn coil or many turns but then they have to be wound closely together so that the coil again has essentially zero length.
By contrast, a solenoid by definition has a long length.

In the case of the coil you get the B field by the Biot-Savart law. For solenoids you use Ampere's law.

Like he said , the formula of the Bcoil is only valid when the coil has zero length or negligible.
and the formula for Bsolenoid is valid when it is of infinite length and infinite turns or say very large, and it would not be riht to say that it depends on the length, it depends on the number of turns per unit length.
So, a coil and a solenoid are essentially two diffeerent things and therefore have different formulae for their magnetic fields.