Solving for Length of Solenoid Wire Using Ampere's Circuital Law

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In summary, Ampere's circuital law is a fundamental law in electromagnetism that states the line integral of the magnetic field around a closed loop is equal to the sum of the enclosed current multiplied by the permeability of free space. It is one of the four Maxwell's equations that relate the magnetic field to the current that creates it. It can only be applied to uniform magnetic fields and is different from Faraday's law of induction, which describes the relationship between the electric field and changing magnetic field. Ampere's circuital law is used in various practical applications, including designing electromagnets, motors, and generators, as well as studying magnetic materials and developing magnetic storage devices.
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Homework Statement


A solenoid of 1.33cm long and 2.6cm in diameter carries a current of 17.8A . the magnetic field inside the solenoid is 22.4 T . find the length of the wire forming the solenoid.


Homework Equations


B= Uo N i / L .


The Attempt at a Solution



the problem is i don't find the value of N? as it cannot be 1 for solenoid. so how do i solve this problem.
 
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You can find the ratio N/L from the field and the current and since you know that L = 1.33 cm, you can find N. Does this help?
 

FAQ: Solving for Length of Solenoid Wire Using Ampere's Circuital Law

1. How is Ampere's circuital law defined?

Ampere's circuital law states that the line integral of the magnetic field around a closed loop is equal to the sum of the enclosed current multiplied by the permeability of free space.

2. What is the significance of Ampere's circuital law in electromagnetism?

Ampere's circuital law is one of the four Maxwell's equations that describe the behavior of electric and magnetic fields. It relates the magnetic field to the current that creates it, making it a fundamental law in electromagnetism.

3. Can Ampere's circuital law be applied to non-uniform magnetic fields?

No, Ampere's circuital law can only be applied to uniform magnetic fields where the strength of the field is constant at all points. In non-uniform fields, the law does not hold true.

4. What is the difference between Ampere's circuital law and Faraday's law of induction?

Ampere's circuital law deals with the relationship between the magnetic field and the current that creates it, while Faraday's law of induction describes the relationship between the electric field and the changing magnetic field. They are two separate laws that are both essential in understanding electromagnetism.

5. How is Ampere's circuital law used in practical applications?

Ampere's circuital law is used in a variety of practical applications, such as designing electromagnets, motors, and generators. It is also used in the study of magnetic materials and in the development of magnetic storage devices, such as hard drives.

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