Magnetic Flux Density in a Circular Loop

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SUMMARY

The discussion centers on calculating the change in magnetic flux density when a single circular loop of wire is transformed into two loops while maintaining the same current. The relevant equation used is B = (μ₀ * N * I) / (2r), where B represents magnetic flux density, μ₀ is the permeability of free space, N is the number of turns, I is the current, and r is the radius. The conclusion is that the magnetic flux density at the center of the loop increases by a factor of 4 when the number of turns is doubled and the radius is halved.

PREREQUISITES
  • Understanding of magnetic flux density and its formula
  • Knowledge of the permeability of free space (μ₀)
  • Familiarity with the concept of current in electrical circuits
  • Basic geometry related to circular loops
NEXT STEPS
  • Study the derivation of the magnetic flux density formula B = (μ₀ * N * I) / (2r)
  • Explore the effects of varying the number of turns in electromagnetic coils
  • Learn about the applications of magnetic flux density in electrical engineering
  • Investigate the relationship between current, radius, and magnetic field strength in circular loops
USEFUL FOR

Students studying electromagnetism, electrical engineers, and anyone interested in the principles of magnetic fields in circular loops.

leena19
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Homework Statement


A current flows in a circular loop consisting of a single turn.If the same wire is bent into a circular loop of 2 turns and the same current is passed through the loop,the magnetic flux density at the centre will change by a factor of ...?
(ans: 4 )


Relevant equations

B = (mu0 * N*I)/2r

The attempt at a solution

For the 1st loop,
B = (mu0 *I)/2r

To find B' after bending,
the length of the wire remains unchanged = 2*pi*r
so to form 2 circular loops the radius has to be halved for each loop?
which makes
B' = (mu0 * N*I)/(2r/2)
B' = (mu0 * 2*I)/(r) ?

so change in flux = B-B'/B
= 3
Thanks in advance.
 
Physics news on Phys.org
flux density at the centre will change by a factor of ...?
Chang by factor means you have to take the ratio, not the difference.
In the problem n will be doubled and r reduces to half.
 
Oh I get it now.
Thank you very much!
 

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