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

In summary, a coil and a solenoid are two different configurations of a current loop, with a coil having a negligible length and a solenoid having a long length. The magnetic field produced by a coil depends on the radius, while the magnetic field produced by a solenoid depends on the number of turns per unit length. The formulas for these fields are different, with Bcoil being μNI/2a and Bsolenoid being μNI/L. Additionally, the presence of a core, such as iron, in a solenoid can enhance its magnetic field. These differences can be further understood by looking at the Biot-Savart law for coils and Ampere's law for solenoids.
  • #1
henry3369
194
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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


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

The Attempt at a Solution


As you can see, the Bcoil depends on the a (radius) while the solenoid depends on L (length).
 
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  • #2
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.
 
  • #3
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.
 
  • #4
rude man said:
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 B
solenoid 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.
 

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

1. What is the difference between a coil and a solenoid?

A coil is a series of loops of wire, while a solenoid is a type of coil that is tightly wound in a cylindrical shape. The terms are often used interchangeably, but a solenoid typically has a higher concentration of magnetic field lines due to its tightly wound shape.

2. How do coils and solenoids create magnetic fields?

When an electric current flows through a wire, it creates a magnetic field around the wire. In a coil or solenoid, the magnetic fields from each individual loop combine and reinforce each other, creating a stronger overall magnetic field.

3. What is the equation for the magnetic field strength of a coil or solenoid?

The magnetic field strength (B) of a coil or solenoid can be calculated using the equation B = μ0 * n * I, where μ0 is the permeability constant, n is the number of turns in the coil, and I is the current flowing through the coil (in amperes).

4. How does the number of turns in a coil or solenoid affect its magnetic field?

The more turns there are in a coil or solenoid, the stronger the magnetic field will be. This is because each turn of wire adds to the overall magnetic field strength, so a higher number of turns results in a higher field strength.

5. What are some practical applications of coils and solenoids?

Coils and solenoids have many practical applications, including electromagnets used in motors, generators, and speakers. They are also used in medical devices such as MRI machines and in industrial equipment for sorting and separating materials. Additionally, they are used in everyday household items like doorbells and electric locks.

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