Magnetic Field due to a current

In summary, the conversation discussed finding the magnetic field at the center of a regular n-sided polygon and deducing the expression for the magnetic field at the center of a circular current by taking the limit as n approaches infinity. The brain suggested using B=(mew)i (cosθ-cosθ)/(4Πd) to find the magnetic field at the center of the polygon, but was unsure how to deduce the expression for a circular current. Through further discussion, it was determined that taking the limits would lead to the correct expression.
  • #1
app
46
0
INTRODUCTION: I had been doing some problems on "Magnetic field due to a current." Now i have one in which one has to find the field at the centre of a regular n-sided polygon. I don't know why I'm not getting it.
THE EXACT PROBLEM: "A regular polygon of n sides is formed by bending a wire of total length 2Πr which carries a current i.(a)Find the magnetic field at the centre of the polygon.(b)By letting n -> infinity, deduce the expression for the magnetic field at the centre of a circular current."
WHAT MY BRAIN SUGGESTED: The first part is allright.The length of each side is (2Πr)/n. Now using B=(mew)i (cosθ-cosθ)/(4Πd), i got the magnetic field at the centre of the polygon as {(mew)i (n^2) sin(Π/n)tan(Π/n)}/2(Π^2)r. But i have no idea how to get part (b).
WHAT I ALSO KNOW:The magnetic field at the centre of a circular current is (mew)i/2a, where a is the radius of the circle. How do we deduce this from the earlier expression?
CONCLUSION:I really don't know how to deduce part (b).Please help. Thanks a lot.
 
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  • #2
app said:
INTRODUCTION: I had been doing some problems on "Magnetic field due to a current." Now i have one in which one has to find the field at the centre of a regular n-sided polygon. I don't know why I'm not getting it.
THE EXACT PROBLEM: "A regular polygon of n sides is formed by bending a wire of total length 2Πr which carries a current i.(a)Find the magnetic field at the centre of the polygon.(b)By letting n -> infinity, deduce the expression for the magnetic field at the centre of a circular current."
WHAT MY BRAIN SUGGESTED: The first part is allright.The length of each side is (2Πr)/n. Now using B=(mew)i (cosθ-cosθ)/(4Πd), i got the magnetic field at the centre of the polygon as {(mew)i (n^2) sin(Π/n)tan(Π/n)}/2(Π^2)r. But i have no idea how to get part (b).
WHAT I ALSO KNOW:The magnetic field at the centre of a circular current is (mew)i/2a, where a is the radius of the circle. How do we deduce this from the earlier expression?
CONCLUSION:I really don't know how to deduce part (b).Please help. Thanks a lot.
For a) express the two angles as a function of the number of sides, n.

Then take the limit as [itex]n\rightarrow\infty[/itex]

AM
 
Last edited:
  • #3
Thanks...

THANKS: Thanks a lot, i got it now.I didn't remember to take the limits.:smile: :smile: :smile:
 

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electrically charged particles, such as electrons, and is measured in units of Tesla (T).

2. How is a magnetic field created by a current?

A current is the flow of electric charge through a conductor, such as a wire. As the electrons in the wire move, they create a circular magnetic field around the wire, with the direction determined by the direction of the current flow.

3. What is the right-hand rule in relation to magnetic fields?

The right-hand rule is a way to determine the direction of a magnetic field created by a current. If you point your thumb in the direction of the current flow, your fingers will curl in the direction of the magnetic field lines.

4. How does the strength of a magnetic field due to a current change with distance?

According to the inverse square law, the strength of a magnetic field due to a current decreases with distance from the current-carrying wire. This means that the farther you are from the wire, the weaker the magnetic field will be.

5. Can a magnetic field due to a current be shielded or blocked?

Yes, a magnetic field due to a current can be shielded or blocked by certain materials, such as iron or steel. These materials have high magnetic permeability, meaning they can redirect or absorb the magnetic field, reducing its strength in the surrounding area.

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