Magnetic Field using Ampere's Law

In summary: However, in general, Ampere's Law is more accurate when dealing with a more complicated geometry.In summary, using Ampere's law allows one to find the magnetic field around a wire, while Biot-Savart law is more convinient in some cases.
  • #1
Hijaz Aslam
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I find Ampere's Circuital Law sort of fishy. I don't understand what the actual theory proposes. And the loop that should be taken into consideration adds much to the confusion. How should we select the loop?

And in the case of a long wire we find the magnetic field around it by applying ##B.2\pi r= \mu_o i_{enc}##. So how do we find the magnetic field due to a short wire (which is not long or infinitely long)?
Using Biot Savart Law we find the magnetic field due to a short wire as ##\mu_o/4\pi r (cos\theta_1-cos\theta_2)##
where ##cos\theta_1## and ##cos\theta_2## are the angles between the length vector (towards the direction of current) and the position vector at the extreme ends.
 
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  • #2
Yes, using Biot-Savart Law is a way to go here. About integration procedures for particular examples ask in math calculus section.
 
  • #3
Hijaz Aslam said:
I find Ampere's Circuital Law sort of fishy. I don't understand what the actual theory proposes. And the loop that should be taken into consideration adds much to the confusion. How should we select the loop?

Fishy ?

As a kid did you never tinker with iron filings and a battery?

Ampere allows one to put a number on this phenomenon...
ironfilingsaroundwire.jpg

http://coe.kean.edu/~afonarev/Physics/Magnetism/Magnetic Fields and Forces-eL.htm

There's no overwhelming reason to chose any particular closed loop path in air
so i'd pick one that makes for a not-very-cumbersome integral

but in solving a practical problem like a transformer ,,

Two%20solenoids,%20B-field_5H15.40_JPG.jpg

https://sharepoint.umich.edu/lsa/physics/demolab/SitePages/5H15.40 - Projection of the Magnetic Field Due to a Current in a Solenoid.aspx

you'd probably find it handy to pick a path through the middle (or centroid) of its iron core.

I guess using a clamp-on ammeter sort of made it intuitive for me...

http://www.sears.com/craftsman-digital-clamp-on-ammeter/p-03482369000P
http://c.shld.net/rpx/i/s/i/spin/image/spin_prod_1113787012?hei=444&wid=444&op_sharpen=1
 
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  • #4
But I would like to know, why do we obtain the answer for a particular case (here, the magnetic field due to a long wire) using Ampere's Law. I mean if we are asked to find the magnetic field due to a short wire how do we do it? (I heard that Ampere's Law is the general rule for finding the magnetic field than the Biot-Savart Law)?
 
  • #5
To call Ampere's law "fishy" is a very bad choice of words. Ampere's Law and Biot-Savart Law are equivivalent in magnetostatics (meaning one can be derived from another). Which one do you choose to use depends on the problem's geometry. In your example of finitely long straight wire, Biot-Savart Law is more convinient to use.
 
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1. What is Ampere's Law?

Ampere's Law is a mathematical relationship between the magnetic field, the current flowing through a closed loop, and the distance from the current to the loop. It is used to calculate the magnetic field around a current-carrying wire or a solenoid.

2. How do you calculate the magnetic field using Ampere's Law?

To calculate the magnetic field using Ampere's Law, you need to find the sum of the current flowing through a closed loop, also known as the line integral, and multiply it by a constant called the permeability of free space. This can be represented mathematically as B = μ0 * I / 2πr, where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the current to the loop.

3. What is the difference between Ampere's Law and Gauss's Law?

Ampere's Law and Gauss's Law are both laws of electromagnetism, but they apply to different aspects. Ampere's Law deals with the relationship between the magnetic field and the current, while Gauss's Law deals with the relationship between the electric field and the electric charge. In simple terms, Ampere's Law is used for calculating magnetic fields, while Gauss's Law is used for calculating electric fields.

4. Does Ampere's Law apply to all situations?

No, Ampere's Law only applies to situations where the current is steady and the electric field is constant. It does not apply to situations where there are changing electric or magnetic fields, such as in the case of electromagnetic waves.

5. What are some real-life applications of Ampere's Law?

Ampere's Law has many real-life applications, including the design of electromagnets, transformers, and electric motors. It is also used in medical imaging, such as MRI machines, which use magnetic fields to produce images of the human body. Ampere's Law is also essential in understanding the behavior of charged particles in particle accelerators, which are used in scientific research.

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